Question

The random variable W has the distribution B(10,1/3). Find
(a) P(W≤2)
(b) P(W=2)
(ii) The random variable X has the distribution B(15, 0.22)
(a) Find P(X=4)
(b) Find E(X) and Var(X)

Answer 1

this a binomial probability right?

Answer 2

yes

Answer 3

so if i am not mistake
\[P(X=k)=\dbinom{n}{k}p^k(1-p)^{n-k}\]
in your case you have
\[P(X=2)=\dbinom{10}{2}(\frac{1}{3})^2(\frac{2}{3})^8\]

Answer 4

need a calculator for this. but
\[\dbinom{10}{2}=\frac{10\times 9}{2}=45\]

Answer 5

\[P(X\leq 2)=P(X=0)+P(X=1)+P(X=2)\]
\[=\left(\frac{2}{3}\right)^{10}+10\left(\frac{1}{3}\right)\left(\frac{2}{3}\right)^9+\dbinom{10}{2}\left(\frac{1}{3}\right)^2\left(\frac{2}{3}\right)^8\]

Answer 6

thank you very much! can't wait to get stats over and done with

Answer 7

i am sure. but these are not that bad, got a formula and a calculator and you should be good to go

Answer 8

it was more understanding how to go about the question... stats is my worst subject im better at the more complicated stuff