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Let Yi, Y2, ..., Yso be a sequence of exponentially distributed random variable with parameter-4 , and Y =/i/40. Find P(Y<2) 40 /mail.google.com/mail/u/0/#inbox/FMcgxwBVCzcfwVpqNzGmrwWBgGqrN?projector-1 &messagePartid=0.2

which way is the simplest way of solving this problem? is there other ways to solve it without using gamma function? if so, please show the different ways! thank you so much !

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Answer #1

Y is sample mean

mean = 4
sd(Y) = 4/sqrt(n) = 4/sqrt(40) = 0.63245
Z = (X - mean)/sd
= (X - 4)/0.63245

P(Y < 2)
= P(Z <( 2 -4 )/0.63245)
= P (Z<−3.16)=0.0008

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