Help Needed!!!

Question

This is my first time working on these problems I'm perplexed!!!

 

Five males with a particular genetic disorder have one child each. The random variable x is the number of children among the five who inherit the genetic disorder. Determine whether the table describes a probability distribution. If it does, find the mean and standard deviation.

   x         0             1          2             3             4             5
P(x)  0.3077   0.4090   0.2174    0.0578    0.0077    0.0004

Answer 1

if P(x) values sum to 1 then it's a probability distribution

that seems to be the case

mean = sum/n = 1/6

standard deviation = square root of variance

variance = average sum of squares of each ( P(x) - mean)

= (P(0) - 1/6)^2 + (P(1) -1/6)^2 + (P(2)-1/6)^2 + (P(3) -1/6)^2 + (P(4) - 1/6)^2 + (P(5) -1/6)^2 all divided by 5. Unless these 5 males are the entire population and not just a sample, then divide by 6