Based on recent polls. NYC Millennial support Sanders at 60% rate. Suppose that

Question

Based on recent polls. NYC Millennial support Sanders at 60% rate. Suppose that a class of 30 consists entirely of Millennials. Find an expression for the expected number of supporters in the class by using the definition of expectation. Write the support by the ith student X_i as a distribution (2 row table). Use b. to find E(X_i). Find the expected number of supporters in the class by using E(sigma X_i) = sigma E(X_i). Find the standard deviation for Sanders support in the class. Extra provide an interpretation for part e.

Explanation / Answer

a) Let X be the r.v of count of supporters out of 30

So X~ Bin( 30, 0.6)

So, E(X) = np = 30 * 0.6 = 18

b) Xi = 0 with probability 0.4

= 1 with probability 0.6

c) E(Xi) = 0* 0.4 + 1* 0.6 = 0.6

d) E(sum Xi) = Sum(EXi) = sum(0.6) = 30 * 0.6 = 18

e) s.d = sqrt(np(1-p) ) = 30 * 0.6 * 0.4 = 18* 0.4 = 7.2

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