SOLUTION: A random variable X has the following probability function define as P(X=x) = {2c, 3c, 4c} where x= {-1, 1, 2} for 2c, 3c and 4c respectively. i. Find the value of c ii. Compute

Algebra ->  Probability-and-statistics -> SOLUTION: A random variable X has the following probability function define as P(X=x) = {2c, 3c, 4c} where x= {-1, 1, 2} for 2c, 3c and 4c respectively. i. Find the value of c ii. Compute       Log On


   

Question 1184198: A random variable X has the following probability function define as P(X=x) = {2c, 3c, 4c} where x= {-1, 1, 2} for 2c, 3c and 4c respectively.
i. Find the value of c
ii. Compute P(X = −1)
iii. Find the standard deviation of X
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!

The sum of the probabilities for all the x values must be 1 --

i. 2c + 3c + 4c = 9c = 1 ===> c = 1/9.

ii. P%28X+=+-1%29+=+2%2F9

iii. mu+=+%28-1%29%2A%282%2F9%29+%2B+1%2A%283%2F9%29+%2B+2%2A%284%2F9%29+=+9%2F9+=+1


===> sigma%5E2+=+E%28X%5E2%29+-+mu%5E2+=+7%2F3+-+1%5E2+=+4%2F3

===> highlight%28sigma+=+2%2Fsqrt%283%29%29