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Lawbutwhere?
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Report Thread starter 12 years ago
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I'm doing S2 (edexcel) and have a hard past exam question, it's just part (c) i cannot do.

The continuous random variable X has probability density function (pdf)

f(x)= x/15 for 0<x<2 (both or equal)

2/15 for 2<x<7 (greater than 2, less than 7)

4/9 - 2x/45 for 7<x<10 (more than or equal to 7,less than or equal to 10)

0, otherwise.

(a) Find expressions for the cumulative distribution function F(x)

(b) Find P(x<or equal 8.2)

(c) Find, to 3 significant figures, E(x).

CHEERS!!
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Spenceman_
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Report 12 years ago
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Do you know HOW to do c) and are making mistakes or do you simply have no idea?
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Spenceman_
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Yeah, the suspense is killing me too:-

You should know that

E(x) = INT( x f(x) )dx

where the integral is from minus infinity to plus infinity.

You have been given what's called a piecewise definition for the p.d.f. Don't be alarmed. You can use exactly the same formula, but you just do the integration in seperate bits, since essentially you have three seperate functions. Also, since f(x) outside of [0,10] you only need worry about that interval. So,

E(x) = INT[0,10]( x f(x) )dx

= INT[0,2](x f(x) )dx + INT[2,7]( x f(x) )dx + INT[7,10]( x f(x) )dx

You should worry (for a microsecond) about the end points of each interval, only to realise that, since P(X = a) = 0 for a continuous random variable, it doesn't matter which inequalities were strict and which weren't. Hopefully you can actually carry out the integration without too much hassle.
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