17. If a random variable X assumes the values 0 and I with P(X= 0) = 3 P(X = 1), then %3D V(X) is : 4 (ii) T (iii) 16 (iv) 16 16

Q: If gcd(m, 28) = 4 and gcd(3,7) = 1 then m = %3D %3D

A: Given: gcdm,28=4  First, we will calculate G.C.D of all options with 28. a gcd4,28=4 ∵ Greatest…

Q: Consider the random variables X, and Y₁ from question B1 again. (a) Show that the sample covariance…

A: a) Recall that the sample covariance between X and Y is defined as: Cov(X,Y) = 1/n * ∑(Xi - x̄)(Yi -…

Q: 14. What is the probability distribution if X ~ B(3,0.82)? P(X = 0) = 0.55 P(X = 1) = 0.36 P(X = 2)…

A:

Q: Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the…

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

Q: 1- If the E (XY) = 3 and the mean of X and Y are both equal to 2, then what is the covariance of the…

A: We have to find covariance.

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

A:

Q: Find Covariance

A:

Q: 4. What is the probability distribution if X ~ B(3,0.82)? О Р(Х — 0) — 0.55 P(X = 1) = 0.36 Р(X — 2)…

A: The p.m.f of the binomial distribution is as follows: Here, n=number of trials p=probability of…

Q: Suppose f(x), the pmf for a discrete random variable X is given in the table below: 10 15 f (x) |…

A:

Q: uted random variables, that is, they are defined on the same sample space. = 5 )=26 Dw.

A: According to guidelines we solve first three subparts when given multiple subparts.

Q: (V) Suppose A and Y are random variables with E. correlation coefficient of X and Y? -x+ 3 and what

A:

Q: 9. A random variable X has the following p.m.f: X0 1 2 3. P J0.1 0.3 0.4 0.2 And F(x) is the cdf for…

A: It is given that the, A random variable X has the pmf as X P(X=x) 0 0.1 1 0.3 2 0.4 3 0.2…

Q: 6x) 0<x<1 S(x)%=D , then p(x<1) is (a) 1 (b) 2 (c) 3 (d) 4 (c) None of these

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

Q: 13. The loss random variable X has a probability generating function 1 P(z) = = 2-z What is E[XA 3]?

A:

Q: of the following is FALSE? (A) E(k³Y) = k³ E(Y) (B) E(1 – k) = 1 – k (C) E(5k Y + 3) = 5k E(Y) + 3…

A:

Q: (a) g(X1, X2, X3) = X1 + 3X2 + 4X3 (b) g(X1, X, X3) = X1 X2 X3

A:

Q: 3. Find a PDF of a random variable X whose CDF is given by Fx(x) = (1-e*)[0,00) (x).

A: Solution

Q: Find (a) the correlation (b) the covariance and (c) correlation coefficient of X and Y

A:

Q: Suppose U = 2T - 1 where T is a geometric random variable with parameter p. What is Var(U)?

A:

Q: 4. For each of the following functions, Find c so that the function is a PDF. a) (cx² + x) 10.11(x).…

A: Solution

Q: Let X be a random variable such that E(X – 2)² = 10 and E(X+ 1)² = 4, then 1 а. Е(X) = - b. E(X) = =…

A: How to obtain E(X) 1. Simplify both expression to get two equation 2. Simplify both equation and…

Q: 7. A discrete random variable X taking non-negative integer values has probability gen- erating…

A:

Q: 1) Assume a relationship Y = g2(91(X)) between the two random variables X and Y where gi and g2 are…

A: @solution::::

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: 2. A random sample X₁, X2, X3 of size 3 is drawn from a population with mean and variance o². Let 01…

A:

Q: Q. 2 For the exponential random variable X with parameter à = 2, compute the ollowing probabilities.…

A:

Q: Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the…

A: Given that ; E(x) = 0            ;     v(x) = 39 E(y) = -4        ;      v(y) = 19 E(z) = 6        ;…

Q: Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the…

A: GivenE(X)=5E(Y)=-7E(Z)=3Var(X)=20Var(Y)=6Var(Z)=23

Q: Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the…

A:

Q: Given that X is a random variable with E(X²) = 16 and Var(X)= 7; find E(X). (A) 9 (B) V3 (C) 3 (D)…

A:

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

A:

Q: Suppose that the random variable, X, is a number on the biased die and the p.d.f. of X is as shown…

A:

Q: 1. A discrete random variable X follows the Uniform distribution if X takes values x = 1, 2, .., N,…

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