problem·3.x is a random variable with an exponential distrbution with parameter

Question

problem·3.x is a random variable with an exponential distrbution with parameter . .6 Thus the ed, of × isx)- 6 e-.6" for x z 0. a) Using the f(x) above and the R integrate function calculate the expected value of X. b) using the dexp function and the R integrate command caloulate the expected value of X. e) e) Calculate 1/.6. How is this related to the above answers? d) Calculate the probability that x > 2. Use the pexp function e) Calculate the probablity that X > 1 standard deviation more than its expected value.

Explanation / Answer

for the question number 2

a) P( z > 2.3 - 2 /4 )

P( z > 0.08) = 0.4681

b)

P( z < 103 - 50*2 / 4 )

P( z < 0.75 ) = 1 - 0.2266 = 0.7734

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