Mathematics, 23.01.2020 06:31 holyturnley

Let and be independent random variables representing the lifetime (in 100 hours) of type a and type b light bulbs, respectively. both variables have exponential distributions, and the mean of x is 2 and the mean of y is 3.

find the joint pdf f(x|y) of x and y.
find the conditional pdf f_2(y|x) of y given x = x.
find the probability that a type a bulb lasts at least 300 hours and a type b bulb lasts at least 400 hours.
given that a type b bulb fails at 300 hours, find the probability that a type a bulb lasts longer than 300 hours.
what is the expected total lifetime of two type a bulbs and one type b bulb?
what is the variance of the total lifetime of two type a bulbs and one type b bulb?

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Let and be independent random variables representing the lifetime (in 100 hours) of type a and type...