If a random variable X has the gamma distribution with 2 a

If a random variable X has the gamma distribution with ? = 2 and ? = 1, find P(1.8 < X < 2.4)

Solution

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if the random variable X has the gamma distribution with aplha = 3 beta = 2 find P(1.6 < X < 2.8)   

Answer

for gamma distribution
F(x) = ?(aplha,beta*x)/(alpha -1)!

?(3,2x) = -(4x^2 + 4x + 2)*e^-2x

P(1.6<X<2.8) = F(2.8) - F(1.6)

= 0.59503068