First slide

Random variable and probability distribution

Question

The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of at least 2 successes is

Easy

A

37/256
B

247/256
C

128/256
D

219/256

Solution

$G i v e n t h a t n p = 4, n p q = 2$
$\begin{matrix} \Rightarrow q = \frac{1}{2}, p = \frac{1}{2}, n = 8 \\ P (x \geq 2) = 1 - P (x < 2) \\ = 1 - [P (x = 0) + P (x = 1)] \\ = 1 - \frac{1}{2^{8}} [^{8} C_{0} +^{8} C_{1}] = \frac{247}{256} \end{matrix} (f o r m u l a P (x = r) = C (n, r) q^{n - r} p^{r}$

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