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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then P(X>1)Suppose that X ~ Unif[0, 1] and let Y = e^X. (a) Find the cumulative distribution function of Y .(b) Find the probability density function of Y .
- Suppose that X is a continuous random variable with density function f(x). If f(x)=k for −5≤x≤3 and f(x)=0 otherwise, determine the value of k.Suppose that the probability density function of x is fx=3x2, 0<x<1 0, elsewhere Determine p(x < (1/3)), p((1/3) ≤ x < (2/3)), and p(x ≥ (2/3)) Determine the cumulative distribution function of x.Suppose that the continuous random variable X has cumulative distribution function given by F(x)= 0, if x < sqrt(2); x2-2, if sqrt(2) <= x <= sqrt(3); 1, if sqrt(3) <= x Find the probability density function of X.
- Suppose that ƒ is a uniform joint probability density function on0 ≤ x 6 2, 0 ≤ y < 3. What is the formula for ƒ? What is theprobability that X < Y?If X is a continuous variable in the range 3 > X > 0 and its distribution function is as follows: F ( x ) = k : ( x3 + x2) find the probability density function?
