Respuesta :
a) The distribution of X is a discrete geometric distribution with pmf p(x) = (5/36)(1/6)^(x-1).b) The theoretical mean (mu) of X is 6.c) The theoretical variance of X is 35.d) The expected value of Y is 6 and the variance of Y is 3.875.
The distribution of X is a discrete geometric distribution, which means that the probability of X taking on any particular value is given by the formula p(x) = (5/36)(1/6)^(x-1). The theoretical mean (mu) of X is 6, which means that on average it should take 6 trials to obtain a sum of 7. The theoretical variance of X is 35, which means that there is a considerable amount of variability in the number of trials needed to obtain a sum of 7. If we consider the random variable Y, the average number of trials needed to roll a sum of 7 based on 25 trials, then the expected value of Y is 6 and the variance of Y is 3.875. This indicates that the average number of trials needed to obtain a sum of 7 is 6 and that the variability decreases as more trials are taken.
a) p(x) = (5/36)(1/6)^(x-1)
b) theoretical mean (mu) of X mu = 6
c) Var(X) = (5/36)*∑x=1∞(1/6)^(x-1)^2 - mu^2
= (5/36)*(1-1/36^2) - 6^2
= 35
d) The expected value of Y , E(Y) = 6
Var(Y) = Var(X/6)
= Var(X)/6^2
= 35/6^2
= 3.875
Learn more about mean here
https://brainly.com/question/15323584
#SPJ4
