3) Suppose X~N(0,1) and Y~N(2,4), they are independent, then is incorrect. 6 X-Y N(-2,5) D Var(X)...
CPoisson can not be determined. distribution P(np) ) Suppose X~N(0,1) and YN(24), they are independent, then (is incorrect. DX+Y-N(2, 5) BP(Y <2)>0.5 -Y-N (-2,5) D Var(X) < Var(Y) 5) Suppose X,Xy..,X, (n>1) is a random sample from N(μ,02) , let-ly, is| then Var(x)- ( Instruction: The followins ass
3) Suppose X,,X,,X, (n > 1) is a random sample from Bernoulli distribution with Circle out your Class: Mon&Wed or Mon.Evening p.mf. p(x)=p"(I-p)'-x , x = 0,1, , thenyi follows ( ). Binomial distribution B(a.p) eNormal distribution N(p,mp(- O Poisson distribution P(np) Dcan not be determined. 4) Suppose X-N(0,1) and Y~N(24), they are independent, then )is incorrect. X+Y N(2, 5) C X-Y-NC-2,5) BP(Y <2)>0.5 D Var(X) < Var(Y) x,X,, ,X, (n>1) is a random sample from N(μσ2), let-1ΣΧί 5) Suppose...
ppolt & Taluom Variable has edf. F(x), then the probability that X lies in the interval [a, b) is Question 2. 30 pt.) Single-choice questions 1) Suppose A and B are independent events, then)is incorrect. P(AIB) = P(A) B P(AB)- P(A) D PCA u B) = P(A) + P(B) e P(A B)-P(A)P(B) 2) Suppose X-Bin(10,0.3) and Y-Bin(15,0.3), they are independent, thenis incorrect. oX+Y-Bin(25,0.3) GX+Y-N(7.5,5.25) D VarX)VarCr) 3) Suppose X N(0,1) and YN(2,4), they are independent, then is incorrecet X +...
is independent of X, and e Problem 3 Suppose X N(0, 1 -2) -1 <p< 1. (1) Explain that the conditional distribution [Y|X = x] ~N(px, 1 - p2) (2) Calculate the joint density f(x, y) (3) Calculate E(Y) and Var(Y) (4) Calculate Cov(X, Y) N(0, 1), and Y = pX + €, where
Let X N(1,3) and Y~ N(2,4), where X and Y are independent 1. P(X <4)-? P(Y < 1) =? 4、 5, P(Y < 6) =? 7, P(X + Y < 4) =?
1. Two normal random variables X and Y are jointly distributed with Var(X) 25 and Var(Y) 1600. It is known that P(Y>80| X = 50) 0.1 and P(Y 22 X 40) 0.7886 (1) What is the correlation coefficient between X and Y? (2) What is the expected value of Y given X 50?
(Sums of normal random variables) Let X be independent random variables where XN N(2,5) and Y ~ N(5,9) (we use the notation N (?, ?. ) ). Let W 3X-2Y + 1. (a) Compute E(W) and Var(W) (b) It is known that the sum of independent normal distributions is n Compute P(W 6)
1. Assume X is Binomial (n, p), where the constant p (0,1) and the integer n > 0. (a) Express PX > 0) in terms of n and p (b) Define Y = n-X. Specify the distribution of Y.
6. Suppose that X and Y are jointly continuous random variables with joint density f(r, y)otherwise (a) Given that X > 1, what is the expected value of Y? That is, calculate Ey X 〉 1).
3. Suppose X ~ Beta(a, β) with the constants α, β > 0, Define Y- 1-X. Find the pdf of Y