If a continuous RVX (> 0) possesses memoryless property, that is P(X>x+h)= P(X > x). P(X > h), then X follows an exponential distribution.
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- If X has an exponential distribution, show thatP[(X Ú t + T)|(x ÚT)] = P(X Ú t)Suppose that the lifetime in years, X, of a type of electrical switch follows the distribution f(x)=12e−x2f(x)=12e−x2for x>0x>0. What type of continuous distribution is this and what is the average lifetime of one of these switches?If the PDF of X is f(x)=2x/k2 for 0<x<k, for what value of k is the variance of X equal to 2?
- suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then P(X>1)For the given Problem, suppose that the probability of concluding that the process is out of control when it is actually in control is set at .02. Find the upper and the lower control limits for the resulting X- chart.Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with λ = 1 Compute P(X≤4) and P(2≤X≤5)
- Use the expected value properties to obtain the E[Y] of the following system : y = 3x + 1 , where E[X] =3The US divorce rate has been reported as 3.6 divorces per 1000 population. Assuming that this rate applies to a small community of just 500 people and it’s Poisson distributed, and that x = the number of divorces in this community during the coming year, determine the following : a. E(x) b. P(x=1) c. P(x=4) d. P(x6) e. P(2x5)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?
- Suppose that a study of a certain computer system reveals that the response time, in seconds, has an exponential distribution with density curve f(x) = (1/3)e(-x/3) for x > 0 and f(x) = 0 otherwise. What is the probability that response time exceeds 5 seconds? What is the probability that response time exceeds 10 seconds?The probability function of the random variable X is defined as f(x)=cx²(1-x)² for 0<x<1, otherwise f(x)= 0. Calculate the constant c , the expected value and the variance.