# Question: The lifetime in years of a manufactured product is Y

The lifetime (in years) of a manufactured product is Y = 5X0.7, where X has an exponential distribution with mean 1. Find the cdf and pdf of Y.

## Relevant Questions

When α and β are integers and 0 < p < 1, we Have Where n = α + β − 1. Verify this formula when α = 4 and β = 3. Let the distribution of W be F(9, 24). Find the following: (a) F0.05(9, 24). (b) F0.95(9, 24). (c) P(0.277 ≤ W ≤ 2.70). The lifetime in months of a certain part has a gamma distribution with α = θ = 2. A company buys three such parts and uses one until it fails, replacing it with a second part. When the latter fails, it is replaced by the ...The number X of sick days taken during a year by an employee follows a Poisson distribution with mean 2. Let us observe four such employees. Assuming independence, compute the probability that their total number of sick days ...Let the independent random variables X1 and X2 be N(0,1) and χ2(r), respectively. Let Y1 = X1/√X2/r and Y2 = X2. (a) Find the joint pdf of Y1 and Y2. (b) Determine the marginal pdf of Y1 and show that Y1 has a t ...Post your question