3. Suppose Y is a random variable with pdff(y) = ay – b, 0 < y < 315Find a and b given that E(Y)=4. Let the pdf of X be given byf(r) = 0.25 exp(-0.25.r), r > 0Show that E(X) = 4 and Var(X) = 165. A multiple-choice examination has 15 questions, each with five possible answers, only one of whichis correct. Suppose that one of the students who takes the examination answers each of thequestions with an independent random guess. What is the probability that he answers at least tenquestions correctly?

Answered: Image /qna-images/answer/6aae6d3b-ef83-4457-ba09-aaa7d41dfd70.jpg

Answered: 3. Suppose Y is a random variable with…

Math

Statistics

3. Suppose Y is a random variable with pdf f(y) = ay – b, 0 < y < 3 %3D 15 Find a and b given that E(Y) •

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: 2- Suppose = {xt)dt . Find ES and d acconding the statistical characteristics of xt).

A: For a continuous random variable X, a probability density function is a function such that (1) f(x)…

Q: 5.4.14. Let Y1, Y2, ... , Yn be a random sample of size n from the pdf fy(y; 0) = ¿e¬y/®, y > 0. Let…

A: Solution(5.4.14)

Q: Suppose that {Y(t), 0 0|Y(1/2) = 0) × .9213. %3D

A: Given information: {Yt, 0≤t≤1} is a Brownian motion process with variance parameter σ2.

Q: 1.4. Let X and Y be independent exponentially distributed random variables with parameter X λ = 1.…

Q: Consider an i.i.d sample of random variable with pdf f(x) = 1 0<X < 0 + 1 then the method of moments…

A: Given functionf(x)=1 ; θ<x<θ+1

Q: The joint PDF of two jointly continuous random variables X and Y is c(x² + y?) for 0 < x <1 and 0 <…

A: We have given that, X and Y two continuous random variables having joint PDF is,

Q: Problem 4) Let X be a continuous random variable with f (x) as its pdf and u as its mean. Prove…

Q: Let X and Y be two random variables with joint pdf f(x,y)=4xy, 0<x<1, O<y<1. Find p(Y<0.5X). 0.5

Q: The joint PDF of the random variables X and Y is constant on the shaded region, as shown in the…

Q: 2.4. Let Y,, Y2, ..., Yn denote a random sample from a uniform distribution with a pdf given by…

Q: Suppose the random variables X and Y have a joint pdf Sxv(a, y) = { *. x+y 0 VY).

A: Given information: The joint probability density function of the random variables X and Y is as…

Q: 6. Let the random variables X and Y have the joint PDF (15x'y 0<x<y<l f(x, y)3D otherwise a. Find…

Q: Let Y1,Y2,.Yn be a random sample from a population with density S9) = { ®ye-1 0 < y< 1, 0<0 < 0…

Q: If we let RX(t) = ln MX(t), show that R X(0) = μ and RX(0) = σ2. Also, use these results to find the…

A: In the theory of probability and statistics, the cumulant generating function (CGF) is sometimes…

Q: X (4) is a WSS process with E [X (t)]=2 and Ryx (T) = 4 + e- 0.1 la, Find the mean 1 and variance of…

Q: 4) - Let y1, Y2, .., y, be a random sample of n observations from an exponential distribution with…

Q: Problem 2 Let X be a continuous random variable with PDF given by fx(=) = e, 1 for all a e R. If Y =…

Q: Suppose that a > 0 is a constant. Let the joint pdf of random variables X, Y be fx,Y (x, y) x > 0, y…

A: To determine the value of the constant a, use the fact that ∫-∞∞∫-∞∞fx,ydydx=1. The conditional…

Q: Consider a random sample X1,..., Xn with n> 3 from the exponential distribution with parameter > 0…

A: Given that X1,X2,......Xn with n>3 from the exponential distribution with parameter λ>0 and…

Q: 4.17 The length of time required by students to complete a one-hour exam is a random variable with a…

A: Given that ; A probability density function is given. By using the properties of continues random…

Q: 9. Let Y1, Y2,., Yn denote a random sample from the probability density function given by 0-1 0<y<3…

A: Solution:- Given that pdf of y f(yθ) = θ yθ-13θ , 0 ≤y≤30 , elsewhere

Q: Consider an i.i.d sample of random variable with pdf f(x) =1 0<x<0 + 1 then the method of moments…

A: In method of moment estimation we equate population moment with sample moment. Now, first order…

Q: 3 If X has the density function (2(x+2) f(x)= -,0<x<1 0, elsewhere. Find the variance of the random…

Q: Let X1 ... Xn i.i.d random variables with Xi ~ U(0,1). Find the pdf of Q = X1, X2, ... ,Xn. Note…

A: It is an important part of statistics. It is widely used.

Q: 1. Let the random variable Y have pdf as f(y\A) = e®=e=t(e-1), y>0,1>0. Show that W = e – 1] ~ x²…

Q: In terms of a positive constant k, random variables X and Y have joint PDF [k+3x² -1/251<1/2, fx,y…

Q: dW is normally distributed, dW has mean zero, dW has variance equal to dt. Parameter other than dw…

A: Since dW is normally distributed, dSS=μdt+σdW can also be considered normally distributed because…

Q: Suppose (X, Y) is bivariate normal with E(X) = 0 = E(Y), Var(X) ² = Var(Y) and a correlation…

A: Given: E [X] = 0 E [ Y] = 0 V [ X] = σ2 V [ Y] = σ2 ρ=0.4 Q=X2+Y-ρX21-ρ2

Q: x and y are random variables with joint PDF ドキツS,メ2D,0 fxiy (x.y) other a) marginal PDF fx(x)? b)…

Q: 4. The joint PDF of two continuous random variables X and Y is given by fx+y 0<x<1, 0<y < 1 S(x, y)…

Q: 4 (30') The continuous type random variables X and Y have joint pdf for 0 <I<4 and 0 <y< 2; 0,…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Consider again a random sample X1,..., Xn from the population distribution with density f (x; 0) =…

Q: Let Y1,...,Yn constitute a random sample from the probability density function given by Г(20)…

Q: Give the marginal probability of (a) X - number of Bars of Signal Strength Y = response time…

A: The marginal probability of ( a ) =?

Q: If X is an exponential random variables with rate 1, then its distribution function is given by…

A: Here it is given that , F(x) = 1 − e−x Let us consider , F(x) = u. Now the distribution function…

Q: 2. Suppose X is a continuous random variable with pdf -즐z if 0 1.0).

Q: - Given the auto correlation function for a stationary ergodic process with no 4. periodic…

Q: The joint PDF of the random variables X and Y is constant on the shaded region, as shown in the…

Q: If X and Y each follow an exponential distribution with parameter 1 and are inde- pendent, find the…

A: Given: X and Y each follow exponential distribution and are independent we want to find pdf of U=X-Y

Q: Problem 4 Let X be a continuous random variable with PDF (# (2=+) (2z + ) 0 < r <1 fx(x) = otherwise…

A: Farmula used V(Y)=E(Y2)-[E(Y)]2

Q: Question# 3: Two random variable X and Y have the joint PDF given by: 2 e-(x+2y) ,0 < x < 0,0 < y <…

Q: Suppose X - Exp(3) with density fx(x) = Bexp(-Bx) for x > 0 nd 3 > 0. For Y = X'/Y, where y>0 is a…

Q: 2. Suppose the joint PDF of X and Y is given by - y²), 0≤x≤ 1, 0 ≤ y ≤ 1 ƒxy(x,y) = {c(x+y³²),…

A: I solved exactly first three subparts because of bartleby policy if you want more please upload…

Q: Let X and Y be two jointly continuous random variables with joint PDF x + y 0 < x, y < 1 fxx (x, y)…

Q: Problem X(t) is a stationary Gaussian random process with ux(t) = 0 and autocorrelation function…

Q: Consider an i.i.d sample of random variable with pdf f(x)= 1 0 <x < 0 + 1 then the method of moments…

A: Solution: From the given information, the probability density function of x is

Q: 1. Let X be a random sample from a population with pdf f(@lx) = ex®-1,0 x0 a. Is Sn sufficient for…

A: We have to find the sufficient estimator of theta and also complete :

Q: Give the marginal probability of (d) * Y = response time (Nearest second) X = number of Bars of…

A: Probability The probability of an event specifies the likelihood of its happening. For example, the…

Q: Two random variable X and Y have the joint PDF given by: J;(x³y+ 1) ,0<x<2,0<ys1 fxy(x,y) = { 4…

Q: 1. Let X and Y be two jointly continuous random variables with joint PDF cy x 0 <y<æ < 1 fxy(x,y) =…

A: "Since you have posted a question with multiple subparts, we will solve first 3 sub-parts for you.…

Question

3. Suppose Y is a random variable with pdf
f(y) = ay – b, 0 < y < 3
15
Find a and b given that E(Y)
=
4. Let the pdf of X be given by
f(r) = 0.25 exp(-0.25.r), r > 0
Show that E(X) = 4 and Var(X) = 16
5. A multiple-choice examination has 15 questions, each with five possible answers, only one of which
is correct. Suppose that one of the students who takes the examination answers each of the
questions with an independent random guess. What is the probability that he answers at least ten
questions correctly?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Multivariate Distributions and Functions of Random Variables$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

If two random variables X and Y are independent with marginal pdfs fx(x)= 2x, 0≤x≤1 and fy(y)= 1, 0≤y≤1 Calculate P(Y/X>2)
Consider a random variable Y with PDF Pr(Y=k)=pq^(k-1),k=1,2,3,4,5....compute for E(2Y)
Consider a real random variable X with zero mean and variance σ2X . Suppose that wecannot directly observe X, but instead we can observe Yt := X + Wt, t ∈ [0, T ], where T > 0 and{Wt : t ∈ R} is a WSS process with zero mean and correlation function RW , uncorrelated with X.Further suppose that we use the following linear estimator to estimate X based on {Yt : t ∈ [0, T ]}:ˆXT =Z T0h(T − θ)Yθ dθ,i.e., we pass the process {Yt} through a causal LTI filter with impulse response h and sample theoutput at time T . We wish to design h to minimize the mean-squared error of the estimate.a. Use the orthogonality principle to write down a necessary and sufficient condition for theoptimal h. (The condition involves h, T , X, {Yt : t ∈ [0, T ]}, ˆXT , etc.)b. Use part a to derive a condition involving the optimal h that has the following form: for allτ ∈ [0, T ],a =Z T0h(θ)(b + c(τ − θ)) dθ,where a and b are constants and c is some function. (You must find a, b, and c in terms ofthe information…
If X1 and X2 constitute a random sample of size n = 2from an exponential population, find the efficiency of 2Y1relative to X, where Y1 is the first order statistic and 2Y1and X are both unbiased estimators of the parameter
Suppose Xis a random variable with E(X) = 2, and E(X2) = 5. Compute the following quantities: a) Var(X) b) E(X−1)2 c) Var(−X−3) d) E(5X+ 4)
Consider two assets (X and Y) with mX = 10%, mY = 10%, σX2=.16, σY2=.25, and Cov(X,Y) = -.125. What is the expected return and variance of the portfolio having 70% invested in X and 30% invested in Y? Compare the risk and return of this portfolio with the risks and returns associated with investing everything in either X or Y. a) What is p(XY)? b) What is the expected return of the portfolio (m.7X+.3Y)? c) What is the standard deviation of the portfolio (s.7X+.3Y)? d) How does the standard deviation of the portfolio (s.7X+.3Y) compare to the standard deviations of assets X and Y? Show all work and formulas used in EXCEL
Suppose X and Y are independent random variables with E(X) =2, E(Y)=3,V(X)=4,V(Y)=16. Finda)E(5X-Y) b)V(5X-Y) c)COV(3X+Y,Y) d)COV(X,5X-Y)
Let us say that we have jointly distributed random variables X and Y with E(X) = 3,E(Y) = 5, Var (X) = 1, Var(Y) = 3, and Cov (X, Y) = 2.Determine:a) E(2X + Y) b) Var(6X)
If marginal denisties was given for two independent random variables f(x)=1/2 for 0<x<2 π(y)=1/3 for 0<y<3 Then find the value of P(X2 + Y2 > 1).