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Question

Statistics Question on Multivariate Distributions

For n∈Nn \in \mathbb{N}, let XnX_n be a random variable having the Bin(n,14)\text{Bin}(n, \frac{1}{4}) distribution. Then
lim⁡n→∞[P(Xn≤2n−3n8)+P(n6≤Xn≤n3)]\lim_{n \to \infty} \left[ P(X_n \leq 2n - \frac{\sqrt{3n}}{8}) + P\left(\frac{n}{6} \leq X_n \leq \frac{n}{3}\right) \right]
is equal to (You may use Φ(0.5)=0.6915\Phi(0.5) = 0.6915, Φ(1)=0.8413\Phi(1) = 0.8413, Φ(1.5)=0.9332\Phi(1.5) = 0.9332, Φ(2)=0.9772\Phi(2) = 0.9772).

A

1.6915

B

1.3085

C

1.1587

D

0.6915

Answer

1.3085

Explanation

Solution

The correct option is (B): 1.3085