The joint pdf of random variables X=1, 2 and Y=1, 2, 3 is P(X,Y)= X 10.05 Find (a) The value of k. (c) P(X>1, Y <2). Y 0.2 0.18 0.15] (b) the marginal probability function of X and Y. (d) Ex, Hy
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![The joint pdf of random variables X=1, 2 and Y=1, 2, 3 is
P(X,Y)= X 10.05
Find (a) The value of k.
(c) P(X>1, Y <2).
Y
0.2
0.18
0.15]
(b) the marginal probability function of X and Y.
(d) Ex, Hy](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa778b651-a5dd-41af-aaa6-c24cbba966ac%2F99d49817-d613-4eaa-9a93-d01fd172db9e%2Fc0kii7_processed.jpeg&w=3840&q=75)
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- If a binomial experiment has probability p success, then the probability of failure is ____________________. The probability of getting exactly r successes in n trials of this experiment is C(_________, _________)p (1p)Find the mean and variance for the probability distribution given by f(x)= 2x k(k+1)* -,x=1,2,3,...kSuppose X and Y have the joint probability distribution P(X = x, Y = y) = c/x+y| for x = -1,0,2 and y = -1,1 (c is a constant), please answer the following questions. (a) What is the value of c? (b) What is the (marginal) probability distribution of X? (c) What is the (marginal) probability distribution of Y?
- Let joint Probability distribution function of random variables X and Y be if (x, y) = (1, 1) 1/3 |1/3 if (x, y) = (0, 0) (1/3 if (x, y) = (2, 0) P(x, y)={ otherwise . Are X and Y independent?k хчу Pcx,y) X=1,2 y=1,2,3 other Find the marginal probability function 5 of Y P (Y)If a discrete random variable X has the following probability distribution: X -2, - 1, 0, 1, 2 P(X) 0.2, 0.3, 0.15, 0.2, 0.15 Use this to find the following: (a) The mean of X and E[X^2]. (b) The probability distribution for Y = 2X^2 + 2 (i.e, all values of Y and P(Y )). (c) Using part (b) (i.e, the probability distribution forY ), find E[Y ]. (d) Using part (a), verify your answer in part (c) for E[Y ]. **Note: Please do not just copy from Chegg!
- 6) (13 points) The random variable X has the following probability density function: x 1x(x)=2 0, for 0C1. Let X be a continuous random variable with PDF f(x) = (2-x) ² for -1 1)? (c) Calculate the expectation of X. (d) Calculate the variance of X.7) For the continuous probability distribution f(x) = kx³e-x Where x 20, find mean.
