(2) Let X be a random variable with a function 3 1 х%3D 0,1, 2,3 4 x! (3-x)! S(x) =- then p(x>2) is o.w 3 27 17 (d) (e) None of these 27 (a) 27 (b) (c) 27 a is the correct answer b is the correct answer c is the correct answer d is the correct answer e is the correct answer

Q: (37) Let X be a random variable with p.d.f. (x+1)e2* x=1,2,3 f(x) =- , find (1) k (2) E(x² +1) O.w

A: The probability distribution table is obtained as :  x 1 2 3 f(x) 2e2k 3e2k 42k Every…

Q: Example 4.1.12 X is a discrete random variable with pmf f (x) given by f(x) = kq* x= 0, 1, 2, . , 0…

A: Answer: Using the given data,

Q: A random variable X is defined by X =- 2 = 3 with a prob. of 113 with a prob. of 1/2 with a prob. of…

A: Given, X -2 3 1 P(X) 1/3 1/2 1/6

Q: Let X be a random variable with E(X) =0 and E(X²) = 2. Then the value of E[X(1– X)] is Select one:…

A:

Q: (1) Let X be a random variable with p.d.f. ke 2x f(x) ={ 0 <x<0 , then o.w (a) k=3 (b) k=2 (c) k =-…

A: Reviewing information, X is a r.v. with pdf, f(x)=k·e-2x                                   ;…

Q: Q3) A) A grocery store sells X hundred kilograms of rice every day, where the distribution of the…

A: Note that X is neither continuous nor discrete

Q: (1) Let X be a random variable with a function [3 |4 х! (3— х)! 1 x = 0,1, 2,3 f(x) = { then E(x) is…

A: Solution: 1. From the given information, the probability function of a random variable X is

Q: 3. Given a discrete random variable X with probability mass function (pmf) fx (x) = {"C Sk(x -6),…

A: Note: According to Bartleby guidelines expert solve only one question and maximum 3 subpart of the…

Q: 5. X and Y are two discrete random variables. If the covariance between X and Y is positive, then:…

A:

Q: .a. X is a discrete random variable that takes values (1, 2, 3, 4, 5). If, P(X=3)=0.5 and F(4)=0.85.…

A: a) It is given that P(X=3) =0.5 and F(4) =0.85.

Q: 7 The discrete random variable X has probability distribution given by (4x +7) P(X= x) = for x= 1,…

A:

Q: 2. If X, Y are independent random variables show that variance (X-Y)= variance (X) + variance (Y).…

A:

Q: (1) Let X be a random variable with a function 3 1 x = 0,1, 2,3 4 х! (3—х)! f(x) = then E(x) is o.w…

A: Let X be a random variable with a function, f(x)=341x!(3-x)!                      ;x=0,1,2,30…

Q: 5. Suppose a random variable (X,Y, Z) is equally likely to take any one of the values (1,0, 0), (0,…

A: Given, Points are equally likely hence,   (X, Y, Z) P (x, y, z) (1, 0, 0) 15 (0, 1, 0) 15…

Q: (4) Let X be a random variable with p.d.f. 2e-2x 0 <x<0 f(x) =• find E(e-2x) O.W

A: Provided probability density function is, fx=2e-2x         for 0&lt;x&lt;∞=0…

Q: (a) Let X and Y be independent random variables both with the same mean u 0. Define a new random…

A: * SOLUTION :-  (1) Based on the above information the calculation is given as follows

Q: Example 8 : A random variable X gives measurements x between 0 and 1 with a 12x - 21x2 +10x, for 0…

A:

Q: (2) Let X be a random variable with p.d.f. (k 1<x<10 S(x) = , then (a) k-2 (b) k-8 (c) k- (d) k-3…

A: according to our guidelines we can answer only  first question and rest can be re posted.

Q: Example 5: Let X1, X2 , X3 and X4 be independent random variables such that E (X;) = µ and Var (X;)…

A:

Q: 2.a) From an urn with 15 red balls and 5 green balls, one ball is drawn with replacement until a…

A: Number of red balls=15 Number of green balls=5 Let, X: Number of trials required until a green ball…

Q: 1. The probability mass function of a discrete random variable X is defined by , x = 0,1,2,3, 1+ kx…

A: Introduction :-  We are given the p.m.f of discrete random variable X We have to find  Value of k…

Q: 1) Let the probability function of a discrete random variable X be 100) = {(²+²) (0.5) (05) 1-²,…

A: Solution

Q: 3.1 Solve the below problem Let Y,, Y2, and Y, be random variables, where E (Y,) = 1, E (Y2) =…

A: Solution is in image uploaded below

Q: 3.) Find P (X > Y) where X and Y are independent random variables that satisfy X~ N (2,1) and Y~ N…

A: We have given the following statement.

Q: 3.1 Solve the below problem Let Y,, Y2, and Y3 be random variables, where E(Y) = 1, E(Y2) V (Y,) =…

A:

Q: (1) Let X be a random variable with a function [3 4 x!(3-x)! S(x) = { 1 x = 0,1, 2,3 , then E(x)is…

A: Solution: Note: Hello! As you have posted 2 different questions, we are answering the first question…

Q: Chebyshev’s inequality (Section 2.4) states that for any random variable X with mean μ and variance…

A: Checbyshev’s inequality: For any random variable X having mean µ and variance σ2,

Q: 4.3.2 The cumulative distribution func- tion of random variable X is (r+ 1)/2 -<r <1, 221. Ex(r) =…

A: The previous part of #b, c, d is not visible. I am able to see #4.3.2 only completely. So, I am…

Q: If a random variable X is defined such that: E[(X – 2)²] = 18 and E[(X+1)²] = 33. Then the values of…

A: The given equations are EX-22=18 and EX+12=33. Now,…

Q: (1) If a random variable X is a constant, i.e.., X =a then E[a]= a, where a is a constant.

A:

Q: Example 8.3.1 Let X1, X, Xạ and X4 be independently and identically distributedN (0, 1) random…

A:

Q: (2) Let X be a random variable with a function 3 1 |4 х! (3-х)! x = 0,1, 2,3 S(x) =- then p(x S 1)…

A:

Q: 3. Let X₁, X2,..., Xn be iid random variables with mean and variance o2. Define the random variable…

A:

Q: Random variables X and Y have a joint PMF described by the following table. y = -1 y = 0 y = 1 1/16…

A: Probability density function explain the probability occurrence of all the observations in a…

Q: 1) Let the probability function of a discrete random variable X be >= {(²9) f(x) = (0.5)*(0.5)16-x,…

A:

Q: the random variable Y is such that : E(2Y+3)=6    and    Var(2-3Y)=11 find      E(Y^2)

A:

Q: 14. Let X be a discrete random variable with the following PMF 1 for k = -2 4 1 for k = -1 Px (k) 1…

A: Farmula used  Range=Maximum-Minimum

Q: oblem-7 et X be a discrete random variable with the following PMF: for a = 0 %3D for x = 1 Px(x) =…

A: See the handwritten solution

Q: 1 Xand Yare independent random variables such that X- Po(3.3) and Y- Po(2.7). Find: a P(X + Y = 5) b…

A: We can find the poisson values either by using the following formula or directly from the poisson…

Q: (a) Let X be a random variable and c is an arbitrary constant. Determine the value of c which makes…

A: Dear students as per guidelines we answer the first question only when multiple different question…

Q: 3.1 Solve the below problem Let Y,, Y2, and Y3 be random variables, where E(Y,) = 1, E (Y,) = 2, E…

A: Note: Hi, thank you for the question. As per our company guideline we are supposed to answer only…

Q: (1) Let X be a random variable with p.d.f. ke 0<x<0 Sx) = ,then O.w (b) k - (e) k- (a) k-1 (c) k (d)…

A: According to our guidelines we can answer only first question and rest can be re posted.

Q: (ii) Find Gx(t) = E (tx) when X is a geometric random variable; i.e. for a {1,2,...} it is that P(X…

A:

Q: (1) Let X be a random variable with a function 3 1 x = 0,1, 2,3 4 x! (3—х)! f(x) =- , then E(x)is…

A:

Q: If a random variable X is defined such that: E[(X – 3)²] = 18 and E[(X+1)²] = 34. Then the values of…

A: The given expectations are EX-32=18 and EX+12=34. Now, EX2+9-6X=18EX2+E9-E6X=18EX2+9-6μ=18EX2-6μ=9…

Q: (3) Let X be a random variable with p.d.f. 2k I<x<10 3x f(x)=- , then o.w (b) - (d) k-2 k - (e) k -…

A:

Q: 13-17. If a random variable X assumes the values 0 and 1 with P(X= 0) = 3 P(X = 1), then nX) is:…

A: Given that, for random variable X,  P(X = 0) = 3P(X = 1) The variance of X ia defined as V(X) =…

Q: 2. Previously, you studied linear combinations of independent random variables. What happens if the…

A: Consider the provided information:μx ≈ 7.34,      σx ≈ 6.55,      μy ≈ 13.19,      σy ≈ 18.57,…

Q: 2.5. Let N be a random variable with distribution function 0 if <0 F(2) = 〈a,2 if 0 < x < 1 Find…

A: Given cumulative ditribution function F(x) as shown belowTo find the P(1/4 &lt; X&lt; 5) According…

Q: Show that if X', Y' are the deviations of the random variables X and Y from their respective means,…

A: In our daily life, we all may come across some situations that one variable that is related to other…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.