Find the value of C for which the following function will be a probability function.
Find the value of C for which the following function will be a probability function. (c)...
7. For the probability density function f(x) = for 0 <<<2 (a) Find P(x < 1) (b) Find the expected value. (c) Find the variance.
(1 point) The joint probability density function of X and Y is given by f(x, y) = cx – 16 c”, - <x< 0 < b < co alt 0 < y < 0 Find c and the expected value of X: c = E(X) =
For what value of the constant c is the function f continuous on ( – 60,00)? f(x) Sca? + 6x if x <3 1 x3 cx if x > 3 C= Preview Question 9 Points norcihlo 1
2. The probability density function of X is given by 10 0,x < 10 a) Find P(X>20). b) What is the cumulative distribution function of X?
(1) Suppose that X is a continuous random variable with probability density function 0<x< 1 f() = (3-X)/4 i<< <3 10 otherwise (a) Compute the mean and variance of X. (b) Compute P(X <3/2). (c) Find the first quartile (25th percentile) for the distribution.
2. Let X have probability density function JX2) = 1/2 0<x< 1 3 < x < 4 otherwise Find the cumulative distribution function of X.
The probability density function of X is given by
0 elsewhere
Find the probability density function of Y = X3
f(r)-(62(1-x)for0 < x < 1
[4+3+3 Points] 9. For the following probability density function, f(x) -k for 0 <x < 0.5 f(x) - 3x2 for 0.5 < x < 1 f(x) -0 otherwise What is the value of k? Find the median value of x Find the probability that X<0.75 a. b.
2. (25 points) For the probability density function (pdn) sGr) rx) =10.08 x (0 5) x 0 (otherwise) (a) Find and sketch the cumulative density function (edr. F(x)-f(x) dx F6) F(x) - (x <0) OsxS5) (x> 5) (b) Find the mean value of x. (c) Find the variance and standard deviation of x 2fx) dx
5. Let X and Y have joint probability density function of the form Skxy if 0 < x +y < 1, x > 0 and y > 0, f(x,y)(, y) = { 0 otherwise. (a) What is the value of k? (b) Giving your reasons, state whether X and Y are dependent or independent. (c) Find the marginal probability density functions of X and Y. (d) Calculate E(X) and E(Y). (e) Calculate Cov(X,Y). (f) Find the conditional probability density function...