Question

1. Stirling’s approximation is n! ~ nⁿ e^-n   What exactly does the   ~    mean?

       b. If a coin is tossed 1600 times, use Stirling to estimate the probability that exactly 800 of the tosses

            land heads.

Answer 1

Answer:

a ) the sign ~ means that the two functions are asymptotic or nearly equal i.e ratio of two functions tends to 1 as n tends to infinity.

ie.

b ) here we use binomial approximation to normal distribution because we knows that for large value of n the binomial distribution tends to normal distribution

here n = 1600 and p = q = 0.5 i.e the probability of coming head(p) and the probability of coming tail (q )

let = 800

now

P(x) =

= ( using z table )

Probability that exactly 800 of tosses lands head is 0.5

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