*Help me pass my Probability test tomorrow*

[bighomage]

Sorry to start an uninteresting thread, but I have a test at 9:45 tomorrow and I have no idea how to do either of these problems, so any help would be greatly appreciated.

1. Let f(x) = a/(x(x+1)(x+2)), x = 1,2,3,...

a. Find a.
b. Find E(x)
c. Find Var(x)

2. X ~ Binomial (n=24, p=0.2). Use binomial theorem to find

a. E(0.7^x)
b. E(0.8^x)

If you can just give me the general gist of how to do these, you'll be my hero.

Also, if anybody knows a good forum where I could post questions like this instead of here, that would be great too.

[evank15]

http://physicsforums.com/

[BruceZ]

[ QUOTE ]
1. Let f(x) = a/(x(x+1)(x+2)), x = 1,2,3,...

a. Find a.
b. Find E(x)
c. Find Var(x)

[/ QUOTE ]

a.) Since f(x) is a probability density function, its sum over all values of x must be 1, so you must adjust a so that this is true. Sum 1/(x(x+1)(x+2)) from 1 to +infinity, and set a equal to 1 over this value.

b.) E(x) is the sum of x*f(x) from 1 to infinity.

c.) Var(x) = E(x^2) - [E(x)]^2. Find E(x^2) by summing x^2 * f(x).


[ QUOTE ]
2. X ~ Binomial (n=24, p=0.2). Use binomial theorem to find

a. E(0.7^x)
b. E(0.8^x)

[/ QUOTE ]

The probability density function for this binomial distribution is

f(x) = C(24,x)*(0.2)^x * (0.8)^(24-x), x = 0,1,2,...24.

Find these expected values by summing 0.7^x * f(x) and 0.8^x * f(x) from 0 to 24.


[ QUOTE ]
Also, if anybody knows a good forum where I could post questions like this instead of here, that would be great too.

[/ QUOTE ]

Probability forum.