# Thread: Dist. of functions of a Random Variable

1. ## Dist. of functions of a Random Variable

Hey, all. Having a rough time with a couple of problems, here's one:

1) If X is chi-squared^2(12); that is, r = 12 sorry dunno the correct notation)

find constants a and b such that P(a <X<b)=0.90 and p(X<a)=0.05

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I think I know how to set it up; the probability is given between a & b, so I need to integrate with bounds a & b, and set the integral equal to 0.9; likewise, I can from 0-->a and set it equal to 0.05

My problem is the integral. Is my pdf correct here:

f(x)= [x^5e^(-x/2)] / (6)(2^6)

So I'd be integrating 1/384* integral of x^5e^(-x/2) ??

How can I do that integral without doing integration by parts 5 times?? Thanks.

2. Originally Posted by amor_vincit_omnia
Hey, all. Having a rough time with a couple of problems, here's one:

1) If X is chi-squared^2(12); that is, r = 12 sorry dunno the correct notation)

find constants a and b such that P(a <X<b)=0.90 and p(X<a)=0.05

---
I think I know how to set it up; the probability is given between a & b, so I need to integrate with bounds a & b, and set the integral equal to 0.9; likewise, I can from 0-->a and set it equal to 0.05

My problem is the integral. Is my pdf correct here:

f(x)= [x^5e^(-x/2)] / (6)(2^6)

So I'd be integrating 1/384* integral of x^5e^(-x/2) ??

How can I do that integral without doing integration by parts 5 times?? Thanks.
Why not use tables of critical values (for 12 degrees of freedom)?

Pr(X < a) = 0.05 therefore ......

Pr(X < b) = 0.95 therefore Pr(X > b) = 0.05 therefore .....

Otherwise you're stuck with the integration ......