Zadanie 1c
Find the least number n of complete years after which its value is below 15% of its original price.
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Find the least number n of complete years after which its value is below 15% of its original price.
For policy A with p=.12, find (i) the probability that the first inspection is on batch 4; (ii) the probability of at least one inspection among the first 8 batches.
(i) Explain why P(X = x) = p(1 − p)x−1 for integer x≥1. (ii) Write E(X) in sigma notation.
For |r|<1, a + ar + ar2 + ⋯ = a/(1 − r). (i) Differentiate both sides with respect to r and express in terms of a,r. (ii) Hence show that E(X)=1/p.
For policy A with p=.12, find E(X) and Var(X).
Show that under policy B the first inspection occurs on batch 3 with probability 405/1024.
Explain why Y≤4.
The distribution of Y is P(Y=1)=1/16,P(Y=2)=m,P(Y=3)=405/1024,P(Y=4)=n. (i) Find m,n. (ii) Show that E(Y)=3019/1024. (iii) Find Var(Y).
(i) Using E(X)=1/p, find p giving E(X)=E(Y). (ii) Find Var(X) for that p. (iii) Which policy gives more consistent inspection intervals at this common mean? Give a reason.
Solve for 0° ≤ x ≤ 120°.