# Probability work | Mathematics homework help

**QUESTION 4**

1. Exercise 4.0a

You are visiting the rainforest, but unfortunately your insect repulsive has run out. As a development, at each assist, a mosquito domain on your neck delay presumption 0.5. If a mosquito domain, it get bite you delay presumption 0.2, and it get never vexation you delay presumption 0.8, inconsequently of other mosquitoes. What is the presumption of substance bit for the 1st era in the 5th assist?

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**2 points **

**QUESTION 5**

1. Exercise 4.0b

You emit n = 10 clear invents, each pretenceing heads delay presumption p_{1} = 0.5, inconsequently of the other emites. Each invent that pretences tails is then emited intermittently, once. Succeeding subjoined this system, what is the presumption that precisely k = 6 invents pretence heads?

Hint: primitive number p_{2},the presumption that a uncompounded invent pretences heads (succeeding subjoined the 2-step system), and then form use of the binomial PMF.

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**2 points **

**QUESTION 6**

1. Exercise 5.3a

Let a uniform unpremeditated shifting X be ardent that takes values in [0, 1], and whose division discharge 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 test typical division