6. In the Pirates of the Aegean video game, you may have to investigate 0, 1, 2, 3, 4, or 5 grottoes without success before you finally loca

Question

6. In the Pirates of the Aegean video game, you may have to investigate 0, 1, 2, 3, 4, or 5 grottoes without success before you finally locate a treasure chest. You conclude that the probability you will have to investigate at mostxgrottoes without success is , and F(5) = 1. (Remember that is the number of permutations(ordered lists withoutreplacement) of kitems from npossibilities.)a) What is the probability you will have to investigate exactly 3 grottoes without success?b) What is the expected numberE(X) of grottoes you will investigate without success?c) What is the variance Var(X) of the number of grottoes you will investigate without success?

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Claire 1 week 2021-10-08T09:40:42+00:00 1 Answer 0

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    2021-10-08T09:42:38+00:00

    Answer:

    a) probability of investigating exactly 3 grottoes = 1/6

    b) E(x) = 2.5

    c) Var(x) = 2.918

    Step-by-step explanation:

    Since there are 6 cases in the distribution, the number of elements in the sample space is 6

    a) probability of investigating exactly 3 grottoes = 1/6

    b) Expected value E(x) = ∈(xP(x))

    E(x) = (0*1/6) + (1*1/6) + (2*1/6) + (3*1/6) + (4*1/6) + (5*1/6)

    E(x) = 2.5

    c) variance of x, Var(x) = ∈ [(E(x) – x)² * P(x)]

    Var(x) = [(2.5-0)²*1/6] +  [(2.5-1)²*1/6] + [(2.5-2)²*1/6] +  [(2.5-3)²*1/6] +  [(2.5-4)²*1/6] +  [(2.5-5)²*1/6]

    Var(x) = 1.042 + 0.375 + 0.042 + 0.042 + 0.375 + 1.042

    Var(x) = 2.918

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