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Math Help - can't figure this one out please help

  1. #1
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    can't figure this one out please help

    Let X1 , X2 , . X7 be a set of seven independent random variables, each
    having the exponential distribution with the mean value of 1, 1/2 , 1/3 , ...,1/7 respectively.
    (a) Find the expected value and standard deviation of their sum T
    ≡ X1 + X2 + ... + X7 .
    (b) What is the probability that min(X1 , X2 , ..., X7 ) > 0.03?
    (c) Find the kurtosis of X1 .
    (d) Compute the expected value of X1^3 /(1+X2 ^2) .
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  2. #2
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    Quote Originally Posted by buddyboy View Post
    Let X1 , X2 , . X7 be a set of seven independent random variables, each
    having the exponential distribution with the mean value of 1, 1/2 , 1/3 , ...,1/7 respectively.
    (a) Find the expected value and standard deviation of their sum T
    ≡ X1 + X2 + ... + X7 .
    (b) What is the probability that min(X1 , X2 , ..., X7 ) > 0.03?
    (c) Find the kurtosis of X1 .
    (d) Compute the expected value of X1^3 /(1+X2 ^2) .
    (a) E(X1 + X2 + ... + X7) = E(X1) + E(X2) + ..... + E(X7).
    Var(X1 + X2 + ... + X7) = Var(X1) + Var(X2) + ..... + Var(X7) since the X's are independent

    (b) It is well known that X(1) = min(X1 , X2 , ..., X7 ) has an exponential distribution with parameter \lambda_1 + \lambda_2 + \, .... \, + \lambda_7 (see Exponential distribution - Wikipedia, the free encyclopedia). Use this pdf to calculate Pr(X(1) > 0.33).

    (c) What definition/type of kurtosis are you using?
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