2. The random variable X has probability density function f given by f(x) 0 otherwise. (a)...
A continuous random variable X has probability density function f(x) = a for −2 < x < 0 bx for 0 < x ≤ 1 0 otherwise where a and b are constants. It is known that E(X) = 0. (a) Determine a and b. (b) Find Var(X) (c) Find the median of X, i.e. a number m such that P(X ≤ m) = 1/2
22. Given a continuous random variable X with probability density function f(x) = {2x, if :05451 otherwise a. Find P(0.3< X< 0.6) b. Find the mean of X C. Find the standard deviation of X.
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise. (a) Find c (b) Find the distribution function Fx) (c) Compute P(l <X<3)
1. Let X be a continuous random variable with probability density function f(x) = { if x > 2 otherwise 0 Check that f(-x) is indeed a probability density function. Find P(X > 5) and E[X]. 2. Let X be a continuous random variable with probability density function f(x) = = { SE otherwise where c is a constant. Find c, and E[X].
3. Let X be a continuous random variable with probability density function ax2 + bx f(0) = -{ { for 0 < x <1 otherwise 0 where a and b are constants. If E(X) = 0.75, find a, b, and Var(X). 4. Show that an exponential random variable is memoryless. That is, if X is exponential with parameter > 0, then P(X > s+t | X > s) = P(X > t) for s,t> 0 Hint: see example 5.1 in...
Given that the random variable X has density function 7. 2x, 0<x <a f(a)-t o, otherwise a) Determine a. Find. P (2 < X < 4) and P (-2 < X < 2 b) Determine the parameter A in PDF given by the formula: f(x) -AeAt. Calculate the probabilities given in the above intervals of x Given that the random variable X has density function 7. 2x, 0
I . (20%) Random variable X has the probability density function as ; Random variable Y 2X+1 0 otherwise a) Determine A b) Determine the Probability Distribution Function F, (x) c) Determine E(X) and ơx d) Determine the probability density function fy(y) and E(Y)
1. A continuous random variable has probability density function f(x) = 2x for all 0 < x < 1 and f(x) = 0 for all other 2. Find Prli <x< 1. O 1 16 O OP O . O 1
The random variable X has the probability density function (x)a +br20 otherwise If E(X) 0.6, find (a) P(X <름) (b) Var(x)
Given is a random variable X with probability density function f given by f(x) = 0 for x < 0, and for x > 1, and f(x) = 4x - 4x^3 for 0 = x = 1. Determine the expectation and variance of the random variable 2X + 3 Expert Answer