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Consider the following function: e if x E [1, 4] f(z) = 26 if x E (4, 10] 0 otherwise Determine { so that f(@) is a probability density function. For that value of &, determine the expected value of a random variable X having f(@) as its density function. 1 = E[X] = _Consider a random variable X with probability density function e if a E [1, 4] f(x) = 26 if x e (4, 10] 0 otherwise with & as determined in the previous question. Determine the cumulative distribution function Fx(t). For t E (-00, 1), Fx(t) = 1 For t E [1, 4], Fx(t) =_ For t E (4, 10], Fx(t) =_ For t E (10, oo), Fx(t) =_