Let X = U(3) find E(3x+7) and distribution function.

Q: Find the relative extrema and saddle points of the function. f (x, y) = x³ – 3xy + y² |

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Q: Q3: Consider the Gaussian Distribution: p(x) = ,-λ (x- a) 2 - Where A and a are constants, Find (x),…

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Q: d) Find the asymptotic distribution for the parameter h(B) = e® assuming that a is known. 0, e2B B…

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Q: 4- Distribution of velocity (DV) of a molecule is given with the following equation DV = ae bv…

A: DV=ae-bv22eD.v2for DV is maximum  Diffrentiate both sides with respect to…

Q: Find B, of the distribution: df = - xe-* 0<x<c0, with u'1=1, Xe-x u'2 = 3, µ'3 =12.

A: Given: Distribution Function: fx=12xe-x,    0&lt;x&lt;∞ Raw moments, μ1'=1μ2'=3μ3'=12 Central…

Q: The linear approximation of e is

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Q: Find the Hessian of the function. Based on result in c), determine the types of stationary points…

A: We need to find the Hessian and stationary points of the function f(x,y)= x3+y2-2xy.

Q: 4- Distribution of velocity (DV) of a molecule is given with the following equation DV = ae…

A: Given Distribution velocity denoted by DV of a molecule as follow: DV=ae-bV2/2eDV2  Where a, b, e, D…

Q: Q1: Let f(x) =2/x^3 ; 1<x<o, zero elsewhere Is p.d.f find 1- The cumulative distribution function…

A: Ans .  f(x) = 2/x3    ;    1&lt;x&lt;infinite   1.   CDF =  P ( X&lt;x )  =  ∫1x2/x^3  dx     = (…

Q: + cx, –1<x<0 , 0<x<3 0, otherwise 15 64 f (x)={-

A: Calculate the value of constant “c” by using the sum property of distribution. So, the density…

Q: Q3 Let X be a continuous random variable with PDF S 4x³ px(x) = 0 < x < 1 otherwise Find E(X) and…

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Q: X₁ and X₂ are random samples from exp(). when x > 0.) (pdf of exp()=e Determine the constant c so…

A: we have given that Xi follow exponential with mean λ that is E(Xi) = λ also, X1 and X2 are…

Q: 6. Find the equation of the normal line to the graph of g(x) = v2-x at x= -7 %3D

A: Definition used -                          The slope of a normal line…

Q: Let Y - X². (a) Find the pdf of Y when the distribution of X is normal N(0, 1). (b) Find the pdf of…

A: Part (a) Express the mathematical relation to calculate the probability density function in normal…

Q: X follows a gamma distribution with PDF  f(x) = 4xe-2x , where X > 0 (a) Derive E(Xn ).

A: Given,  fx=4xe-2x, x&gt;0 Therefore, Exn=∫0∞xnfxdx=∫0∞xn×4xe-2xdx=∫0∞4×xn+1e-2xdx=4×∫0∞xn+2-1e-2x dx

Q: Find all Max., Min., Saddle point for the functions below: P(x) = 2xy-5x²-29² + 4x +49-4

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Q: Find the mean, variance and the coefficients B1, B2 of the distribution : dF = kx²e* dx = 1,0 < x…

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Q: The joint PDF of the random variables X and Y is defined as f(x, y) = 25e: 00 = 0, otherwise (i)…

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Q: 11) If X be a r.v. from exponential distribution (x)= e- ス>0, x20 Then the moment generating…

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Q: (a) Find the marginal PDFS fx(x) and fr(y). (b) What are E X and Var X? (c) What are EY and Var|Y?

A: Provided information is, The random variable X and Y have joint PDF as: fx,yx,y=x+y3      0≤x≤1=0…

Q: the conditional pdf of Y given X.

A: The joint pdf is  f(x,y)=k(x+y)    0≤x≤y≤10             otherwise  then value of k…

Q: Find the correlation co-efficient between X and Y, which are jointly normally distributed with 1 1…

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Q: Find the marginal PDFS fx (x) and fy(y).

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Q: T has an exponential distribution such that P(TS2)=2P(T>4) What is Var(T)=

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Q: Q4-Find the distribution function associated with f(x) = , for 0 < x < 1 or 2 < x < 4, and zero…

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Q: LetX1,X2,...,Xn be a sequence of independent and identically distributed random variables having the…

A: It is known that E(Xi) =1/λ and Var(Xi) =1/( λ2) EY=EX1+X2+...+Xn         =EX1+...+EXn…

Q: 1. Let X be an RV with PDF - f(x) = {1 = |x| a. Find the mean of g(x) = 5x² - 1. b. Find the…

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Q: iv) Explain why, in this instance, the correlation of X and Y,p(X,Y), is equal to the covariance of…

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Q: (a) (b) (c) (d) (e) (f) 0 otherwise Find the cumulative distribution function F(x) P(X ≤ 2) P(X 2)…

A: Given: The pdf of discrete random variable X is f(X)=16  ; X=0,213 ; X=1,30   otherwise We have to…

Q: Let X ~ U[0,1] and Y = -βln(1-X). What is the distribution of Y? Justify.

A: Solution

Q: Let X be the service time which follows exponential distribution with parameter 1 = 0.2. Find the…

A: Given that:  X be the service time having λ=0.2

Q: d) Find the asymptotic distribution for the parameter h(B) = e® assuming that a is known.

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Q: If Y Poisson(A) and A has pdf f(A) = e-^ for A > 0, elsewhere, find zero E(2Υ) V (2Y):

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Q: F (x) = c du for x e R. For what value of c is F a distribution function?

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

Q: The time, X, to infection for Eagle Flu in minutes, after coming into contact with the virus has…

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Q: Determine the equation of the normal line at the given x-value. 1) g(x) = x5, x = 2 2) f(x) = 3x3 −…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let X|Λ have an exponential distribution with conditional survival function SX|Λ(x|λ) = e−λx. Let Λ…

A: Exponential Distribution: If a continuous random variable X is said to be follow exponential…

Q: Find the local extreme values and saddle point of the function f(x, y) = 2x3 + 2y3 – 9x² + 3y² – 12y

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Q: Consider the process X(t) = W(t) + t. What is the probability that it ever reaches the value-1?…

A: Given: Let us consider the given process Xt=Wt+t To determine: The probability that it ever reaches…

Q: f(x)= k(3x+4), x = -1,0,1,2 Find expected value E(X) .

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Q: x2.2 Suppose that the Lorenz Curve for country A is given by YA = x* and for country B is yB mine…

A: The graph of cumulative distribution of percentage of population vs cumulative distribution of…

Q: Let X denote the temperature at which a certain chemical reaction takes place. Suppose that  X has…

A: Given : Pdf of X : f(x) =194-x2     -1≤x≤20                       0.w

Q: ) Determine the value of C. ) Find the marginal PDF of X. -) Find the conditional PDF of Y given X =…

A: The conditional density of Y given X = x can be obtained as f(y | X = x) = f(x, y)/fX(x) Note :…

Q: f(x) = Ae (x-b)2 2a2 - f(x) z e° ze-x²

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Q: If (a,B) is a saddle point of the function f(x,y)=27y2-y3+3x²-6xy, then a+ß=

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Q: a) Find the marginal pdf's of X1 and X2 b) Are X1 and X2 independent? Why or why not? c) Find P(X1 <…

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Q: If (a,B) is a saddle point of the function f(x,y)=21y2-y3+3x2-6xy, then a+ß=

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Q: 4- Distribution of velocity (DV) of a molecule is given with the following equation DV = ae bv-…

A: Distribution of velocity (DV) of a molecule is given with the following equation

Q: 2.7 For an exponential distribution fx(x; p) = {ue *; (iz %3D e. w. where u

A: Given density function, This is the exponential distribution with parameter μ. a) Mean: b)…

Q: Fou are given the Posterior pdf fesp[-(8-x)]. e >x = (x\e)c [0. e <x ind (as a function of x) the…

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

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!