7. For the probability density function f(x) = for 0 <<<2 (a) Find P(x < 1)...
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
2) Suppose that X has density function f(a)- 0, elsewhere Find P(X < .3|X .7).
1. Consider the joint probability density function 0<x<y, 0<y<1, fx.x(x, y) = 0, otherwise. (a) Find the marginal probability density function of Y and identify its distribution. (5 marks (b) Find the conditional probability density function of X given Y=y and hence find the mean and variance of X conditional on Y=y. [7 marks] (c) Use iterated expectation to find the expected value of X [5 marks (d) Use E(XY) and var(XY) from (b) above to find the variance of...
Let f(x,y) = exp(-x) be a probability density function over the plane. Find the probabilities: Parta)P( X2 + y2 <a), a > 0, Part b)P(x2 + y2 <a), a > 0.
121 Q1. If x is continuous variable and follows probability density function x/7; 2<x<4 f(x) = then find the value of P(2<x<3) ? 0; otherwise
Suppose that the probability density function of X is f(x) {cx3 0 1< x < 5 otherwise where c is a constant. Find P(X < 2).
Suppose that the probability density function of X is f(x) {cx3 0 1< x < 5 otherwise where c is a constant. Find P(X < 2).
5. Given the probability density f(x)= for -0<x<00, find k. 1+ 2 Jor -
(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.
Consider the probability density function 0 ifr <0 8.77 if 0 < x <1 0 if > 1 Find the median. Enter your answer to 3 decimal places. Answer: