# Probability work

**QUESTION 4**

1. Exercise 4.0a

You are visiting the rainforest, but unfortunately your insect repulsive has run out. As a termination, at each prevent, a mosquito demesne on your neck behind a while appearance 0.5. If a mosquito demesne, it earn bite you behind a while appearance 0.2, and it earn never annoy you behind a while appearance 0.8, unconnectedly of other mosquitoes. What is the appearance of being bit for the 1st term in the 5th prevent?

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**2 points **

**QUESTION 5**

1. Exercise 4.0b

You throw n = 10 equitable counterfeits, each professioning heads behind a while appearance p_{1} = 0.5, unconnectedly of the other throwes. Each counterfeit that professions tails is then throwed again, once. Behind forthcoming this regularity, what is the appearance that accurately k = 6 counterfeits profession heads?

Hint: leading apportion p_{2},the appearance that a individual counterfeit professions heads (behind forthcoming the 2-step regularity), and then perform use of the binomial PMF.

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**2 points **

**QUESTION 6**

1. Exercise 5.3a

Let a consistent purposeless fickle X be loving that takes values in [0, 1], and whose dispensation duty F satisfies

F(x) = 2x^{2} − x^{4} for 0 ≤ x ≤ 1

a. Compute P (1/4 ≤ X ≤ 3/4 )

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**QUESTION 10**

1. Exercise 5.14

Determine the 10th percentile of a exemplar typical dispensation