Let X ~ Bin(n, p). Show that if x is an integer between 1 and n inclusive, then a. P(X = x) P(X = x- 1) (2+1)() - x + b. Show that if X - Bin(n, p), the most probable value for X is the greatest...

Let X ~ Bin(n, p).<br>Show that if x is an integer between 1 and n inclusive, then<br>a.<br>P(X = x)<br>P(X = x- 1)<br>(2+1)()<br>- x +<br>b.<br>Show that if X - Bin(n, p), the most probable value for X is the greatest integer less<br>than or equal to np + p. [Hint: Use part (a) to show that P(X = x) 2 P(X = x -<br>1) if and only if x < np + p.]<br>

Extracted text: Let X ~ Bin(n, p). Show that if x is an integer between 1 and n inclusive, then a. P(X = x) P(X = x- 1) (2+1)() - x + b. Show that if X - Bin(n, p), the most probable value for X is the greatest integer less than or equal to np + p. [Hint: Use part (a) to show that P(X = x) 2 P(X = x - 1) if and only if x < np="" +="">

Jun 10, 2022

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Let X ~ Bin(n, p). Show that if x is an integer between 1 and n inclusive, then a. P(X = x) P(X = x- 1) (2+1)() - x + b. Show that if X - Bin(n, p), the most probable value for X is the greatest...

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