Probability work | Mathematics homework help
1. Exercise 4.0a
You are visiting the rainforest, but unfortunately your insect repulsive has run out. As a product, at each promote, a mosquito rank on your neck behind a while likelihood 0.5. If a mosquito rank, it get bite you behind a while likelihood 0.2, and it get never stir you behind a while likelihood 0.8, unconnectedly of other mosquitoes. What is the likelihood of life bit for the 1st spell in the 5th promote?
1. Exercise 4.0b
You hurl n = 10 unspotted invents, each illusioning heads behind a while likelihood p1 = 0.5, unconnectedly of the other hurles. Each invent that illusions tails is then hurled again, unintermittently. Behind forthcoming this way, what is the likelihood that correspondently k = 6 invents illusion heads?
Hint: principal weigh p2,the likelihood that a separate invent illusions heads (behind forthcoming the 2-step way), and then fashion use of the binomial PMF.
1. Exercise 5.3a
Let a consistent purposeless capricious X be ardent that takes values in [0, 1], and whose classification office F satisfies
F(x) = 2x2 − x4 for 0 ≤ x ≤ 1
a. Compute P (1/4 ≤ X ≤ 3/4 )
1. Exercise 5.14
Determine the 10th percentile of a model recognized classification