Question: The continuous random variable T has probability density function f (t) = kt ^ 2 for 1 x 0 and 0 elsewhere. a) Determine the

The continuous random variable T has probability density function f (t) = kt ^ 2 for 1 x 0 and 0 elsewhere.

a) Determine the value of k

b) Find the cumulative distribution function of X

c) Calculate the probability that T takes a value of at least -1/2

d) Find the mean and standard deviation of the values of T

e) Find the maximum value of 87% of the values that T can take

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