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S1 Expectation of discrete random variable question Watch

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    Really stuck on this! Wondering if anyone could help me?

    The random variable T has mean 20 and standard deviation 5. It is required to scale T by using the transformation S=aT+b, where a and b are constants (a>0), so that E(s) = 100 and Var (S) = 225

    I created 2 simultaneous equations -

    1) 100=20a+b
    2) 225=25a+b
    therefore 5a = 125, a=25
    and b= 225-625 = -400

    But the answer is a=3 and b=40

    Why am I wrong? (thanks in advance)
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    (Original post by duskflower)
    Really stuck on this! Wondering if anyone could help me?

    The random variable T has mean 20 and standard deviation 5. It is required to scale T by using the transformation S=aT+b, where a and b are constants (a>0), so that E(s) = 100 and Var (S) = 225

    I created 2 simultaneous equations -

    1) 100=20a+b
    2) 225=25a+b
    therefore 5a = 125, a=25
    and b= 225-625 = -400

    But the answer is a=3 and b=40

    Why am I wrong? (thanks in advance)
    Your second equation is incorrect.

    Var(S) = a^2 Var(T)
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    (Original post by ghostwalker)
    Your second equation is incorrect.

    Var(S) = a^2 Var(T)
    thanks! that makes sense x
 
 
 
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