# Question: Let X have probability density fX Find the probability density

Let X have probability density fX. Find the probability density function of the random variable Y defined by Y = aX + b.

**View Solution:**## Answer to relevant Questions

Find the probability density function of Y = eX when X is normally distributed with parameters μ and σ2. The random variable Y is said to have a lognormal distribution (since log Y has a normal distribution) with ...The joint probability density function of X and Y is given by f (x, y) = e−(x+y) 0 ≤ x < ∞, 0 ≤ y < ∞ Find (a) P{X < Y} (b) P{X < a}. The joint density of X and Y is given by (a) Are X and Y independent? If, instead, f (x, y) were given by (b) Would X and Y be independent? The gross weekly sales at a certain restaurant is a normal random variable with mean $2200 and standard deviation $230. What is the probability that (a) The total gross sales over the next 2 weeks exceeds $5000; (b) Weekly ...Repeat Problem 2 when the ball selected is replaced in the urn before the next selection. Problem 2 Suppose that 3 balls are chosen without replacement from an urn consisting of 5 white and 8 red balls. Let Xi equal 1 if the ...Post your question