The lifetime (in days) of a certain electronic component that operates in a high-temperature environment is lognormally distributed with μ = 1.9 and σ = 0.4.     Find the probability that a component lasts between three and six days

Calculate the expected value E(X) of the given random variable X. X is the number of tails that come up when a coin is tossed 26 times. E(X) =

Suppose that X has a lognormal distribution with parameters 0 = 2 and w² = 9. Determine the following. %3D (a) Round the answer to 3 decimal places. P(X 1000. Round the answer to 2 decimal places.

Assume that 1 out of every 5 adults in a local community is unemployed. Approximatethe probability that in a random sample of 100 adults from the community, more than 25are unemployed. Express your final answer in terms of the standard normal cumulativedistribution function Φ.

Let X∼Uniform(0,1) distribution. Find the PDF of Y= 3√X and derive the expected value and the variance of Y.

Let random variable X denote the length of a wire, assumed to be exponentially distributed with mean 107 cm. The wire is cut to make rings of radius 1 cm. Derive the probability mass function for the number of complete rings that can be produced by each length of wire.

Show work for every step. Two types of customers (Preferred and Regular) call a service center. Preferred customers call with rate 3 per hour, and Regular customers call with rate 5 per hour. The interarrival times of the calls for each customer type are exponentially distributed. If the call center opens at 8:00 AM, what is the probability that the first call (regardless of customers type who calls) is received before 8:15 AM?

Let X be a Poisson random variable with rate X. Find the mgf of X.

Assume the time required to fully recharge an electric car is uniformly distributed between 160 and 220 minutes.  What is the expected charge time, E(x)?

You are planning to go fishing with two friends. The time (in hours) before you catch a fish is exponentially distributed with parameter 6. How long do you need to arrange for the fishing so that there is a 95% probability that everyone catches at least one fish? [Assume that the events that each person catches a fish are independent.]