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Suppose X has a binomial distribution B(...

Suppose X has a binomial distribution `B(6,""""1/2)` . Show that `X" "=" "3` is the most likely outcome. (Hint: `P(x=3)` is the maximum among all `P(x_i),""x_i=0,""1,""2,""3,""4,""5,""6)`

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In a binomial distribution `B(6,1/2)`,
`n = 6 and p = 1/2`
Here, `n` is number of the trials and `p` is the success probability of each trial.
`:. q = 1- 1/2 = 1/2.`
Now, `P(X = k) = C(6,k) (1/2)^k(1/2)^(6-k) = (1/2)^6 C(6,k)`
So, most likely outcome will have maximum value of `C(6,k)`.
When `k = 0, C(6,0) = 1`
When `k = 1, C(6,1) = 6`
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