Let X1 be a binomial random variable with n1 trials and p1 = 0.2 and X2 be an independent
binomial random variable with n2 trials and p2 = 0.8. Find the probability function of
Y = X1 + n2 – X2.
Exactly how does one calculate the mgf of (n2 - X2)?
Hi, I've no idea where to go with the question below:
Joint moment generating function of X and Y - MXY(s,t) = 1/(1-2s-3t+6st)
for s<1/2, t<1/3.
Find P(min(X,Y) > 0.95) and P(max(X,Y) > 0.8)
So is this how it goes, based on the given values of x and P(X=x):
P(|X-2.31| >= 1.074)
= P( X-2.31 >= 1.074) + P( 2.31-X >= 1.074)
= P( X >= 3.384) + P( X <= 1.236)
= 0.16 + 0.19 + 0.04
= 0.39
I only managed this much:
Expected value = 2.31
Standard deviation = 1.074
P( |X - 2.31| >= 1.074)
=P( -1.074 >= (X - 2.31) >= 1.074 )
=P( 1.236 >= X >= 3.384)
I'm stuck here. For question b, I assume I have to calculate the expected value of C by substituting the variables x and x^2...
The following table gives the probability distribution of X, the number of defective products in a production line in a day.
x P(X=x)
0 0.04
1 0.19
2 0.35
3 0.26
4 0.16
a. Evaluate P(|X - expected value| >= standard dev)
b. The...
I'm using the mgf of exponential: lambda/(lambda -t). So, to obtain the probability, simply integrate the probability density function of X with the values of a1 and b1, is that it?
From the pdf of X, f(x) = 1/8 e^-x/8, x > 0, find the mgf of Y=X/4 +1. What is then the value of P(2.3 < Y < 4.1)?
Homework Statement Homework Equations
Moment generating function of exponential distributionThe Attempt at a Solution
I have the mgf of X, which is 1/8 / (1/8 - t). I have also...