Question: A continuous random variable X has density function (i) Obtain the value of c. (ii) Calculate the probabilities P(0 (iii) Find the distribution function, F(x),

A continuous random variable X has density function 0. x < 0, e-x/4 f(x)= 0x2, 4 2c X 2. (x+3)5'

(i) Obtain the value of c.
(ii) Calculate the probabilities P(0 (iii) Find the distribution function, F(x), of X. Is it true that F′(x) = f (x) for all real x? Explain.

0. x < 0, e-x/4 f(x)= 0x2, 4 2c X 2. (x+3)5'

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