This year, the number of accidents, X, at an amusement park has probability generating function PX (t) = e−0.2(1−t) , where defined.
The amusement park owner’s insurance company reimburses up to a maximum of one accident this year. Let Y be the number of unreimbursed accidents.
Determine the probability generating function, PY (t) , of the number of unreimbursed accidents at this amusement park this year, where defined.
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This year, the number of accidents, X, at an amusement park has probability generating function PX (t) = e−0.2(1−t) ,...
This year, the number of accidents, X, at an amusement park has probability generating function PX (t) = e−0.2(1−t) , where defined. The amusement park owner’s insurance company reimburses up to a maximum of one accident this year. Let Y be the number of unreimbursed accidents. Determine the probability generating function, PY (t) , of the number of unreimbursed accidents at this amusement park this year, where defined.
3. Use the probability generating function Px)(s) to find (a) E[X(10)] (b) VarX(10)] (c) P(X(5)-2) . ( 4.2 Probability Generating Functions The probability generating function (PGF) is a useful tool for dealing with discrete random variables taking values 0,1, 2, Its particular strength is that it gives us an easy way of characterizing the distribution of X +Y when X and Y are independent In general it is difficult to find the distribution of a sum using the traditional probability...
4. The number of claims per week at an Suppose that Y has probability mass function insurance company is a random variable Y Pr(v),0,1,2. py(y) 0, otherwise. The moment generating function (mgf) of Y is given by my(t)-c(1-e2)- for values of t<2. You do not need to prove this. (a) Show that c1-2 (b) What is the probability that there are at least 2 claims in a given week? (c) Find E(Y)
A policyholder has a two-year auto insurance for his new car. Let X be the number of accidents that the policyholder experiences in one year. You are given: Pr[X = 0] = 0.9 Pr[X = 1] = 0.08 Pr[X = 2] = 0.02 The number of accidents that the policyholder experiences in each year is independent. Given that the policyholder experiences exactly 2 accidents in two years, find the probability that the policyholder experiences at least one accident in each...
The moment generating function ф(t) of random variable X is defined for all values of t by et*p(x), if X is discrete e f (x)dx, if X is continus (a) Find the moment generating function of a Binomial random variable X with parameters n (the total number of trials) and p (the probability of success). (b) If X and Y are independent Binomial random variables with parameters (n1 p) and (n2, p), respectively, then what is the distribution of X...
2. Let Xand Y be random variables with joint moment generating function M(s,t) 0.3+0.1es + 0.4e +0.2 es*t (a) What are E(X) and E(Y)? (b) Find Cov(X,Y)
2. Let Xand Y be random variables with joint moment generating function M(s,t) 0.3+0.1es + 0.4e +0.2 es*t (a) What are E(X) and E(Y)? (b) Find Cov(X,Y)
12. let Mx(1) be the moment generating function of X. Show that (a) Mex+o(t) = eMx(at). (b) TX - Normal(), o?) and moment generating function of X is Mx (0) - to'p. Show that the random variable 2 - Normal(0,1) 13. IX. X X . are mutually independent normal random variables with means t o ... and variances o, o,...,0, then prove that X NOEL ?). 14. If Mx(1) be the moment generating function of X. Show that (a) log(Mx...
Problems binomial random variable has the moment generating function ψ(t)-E( ur,+1-P)". Show, that EIX) np and Var(X)-np(1-P) using that EXI-v(0) and Elr_ 2. Lex X be uniformly distributed over (a b). Show that EX]- and Varm-ftT using the first and second moments of this random variable where the pdf of X is () Note that the nth i of a continuous random variable is defined as E (X%二z"f(z)dz. (z-p?expl- ]dr. ơ, Hint./ udv-w-frdu and r.e-//agu-VE. 3. Show that 4 The...
problems binomial random, veriable has the moment generating function, y(t)=E eux 1. A nd+ 1-p)n. Show that EIX|-np and Var(X) np(1-p) using that EIX)-v(0) nd E.X2 =ψ (0). 2. Lex X be uniformly distributed over (a b). Show that ElXI 쌓 and Var(X) = (b and second moments of this random variable where the pdf of X is (x)N of a continuous randonn variable is defined as E[X"-广.nf(z)dz. )a using the first Note that the nth moment 3. Show that...
Activity: A Journey Through Calculus from A to Z sin(x-1) :- 1) x< h(x) kr2 - 8x + 6. 13x53 Ver-6 – x2 +5, x>3 Consider f'(x), the derivative of the continuous functionſ defined on the closed interval -6,7] except at x 5. A portion of f' is given in the graph above and consists of a semicircle and two line segments. The function (x) is a piecewise defined function given above where k is a constant The function g(x)...