Suppose that X = log(Y ) and that X ∼ N(0.5, 0.16). What is the probability of P(Y > 1)?
Suppose that X = log(Y ) and that X ∼ N(0.5, 0.16). What is the probability...
Suppose that X ∼ N(-1.9,2.9), Y ∼ N(3.0,1.7), and Z ∼ N(0.5, 0.6) are independent random variables. Find the probability that |2.0X + 3Y + 4Z| ≤ 10.1. Round your answer to the nearest thousandth.
Given that log x=2, log y = 4, and log 3-0.5, evaluate the following expression without using a calculator log (3x?y) log (3x?y) - (Type an integer or a decimal.) o Enter your answer in the answer box Type here to search c W
Calculate the probability mass function of Z = X + Y where X and Y are statistically independent and identically distributed binomial random variables with N = 2 and p = 0.4 . The probability mass functions for X and Y are P ( X = j ) = P ( Y = j ) = ( 2 j ) ( 0.4 ) j ( 0.6 ) 2 − j = { 0.36 j = 0 0.48 j = 1...
For two bivariate normal random variables X~N(0,1), Y~N(5,1), and CovX,Y=-0.5, answer the following questions: Compute P(Y>5|X=1) Compute P(Y>5|X=-1) Explain why the computed probability in b is greater than that in a. Compute P(2X-Y>-3).
f(x,y)=0 2. (20 marks) Suppose X and Y are jointly continuous random variables with probability density function fc, 0<x<1, 0<y<1, x + y>1 else a) (2.5 marks) Find the constant, c, so that this is valid joint density function. b) (5 marks) Find P(Y > 2X). c) (5 marks) Find P(X>0.5 Y = 0.75). d) (5 marks) Find P(X>0.5 Y <0.75). e) (2.5 marks) Are X and Y independent? Justify your answer citing an appropriate theorem.
4. (20 pts.) [Bonus Question) Suppose that X is a Binomial RV with p=0.5 i.e. X ~ Bin(n,0.5). Find the probability mass function of the transformation Y = 2X.
f(x,y)= 0 1. (15 marks) Suppose X and Y are jointly continuous random variables with probability density function 12, 0<x<1, 0<y<0.5 else a) (5 marks) Find P(X - Y <0.25). b) (5 marks) Find P(XY <0.30). c) (5 marks) Find V (2x - 5Y+30).
Suppose that X and Y are jointly continuous random variables with joint probability density function f(x,y) = {12rºy, 1 0, 0<x<a, 0<y<1 otherwise i) Determine the constant a ii) Find P(0<x<0.5, O Y<0.25) HE) Find the marginal PDFs fex) and y) iv) Find the expected value of X and Y. Le. E(X) and E(Y) v) Are X and Y independent? Justify your answer.
3. Suppose that X is normally distributed N(3.6,0.81).IfY a. Find the probability density function for Y b. State the mean and the expected value for Y c. Calculate the probability P(120S YS 520).
2) Conditional probability distribution of X given y 1 and yo17 C) 0.5 x/ 2) Conditional probability distribution of X given y 1 and yo17 C) 0.5 x/