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
A continuous random variable X has probability density function f(x) = a for −2 < 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...
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(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.
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