Question

In: Math

100 losses are independent, identically distributed, with a common uniform distribution over (0, 6). Using the...

100 losses are independent, identically distributed, with a common uniform distribution over (0, 6). Using the normal approximation, calculate the probability that the sum of all the losses (the aggregate loss) will exceed 275.

Solutions

Expert Solution


Related Solutions

Let Z1, Z2, . . . , Zn be independent and identically distributed as standard normal...
Let Z1, Z2, . . . , Zn be independent and identically distributed as standard normal random variables. Prove the distribution of ni=1 Zi2 ∼ χ2n. Thanks!
Let ?1 , ?2 , ... , ?? be independent, identically distributed random variables with p.d.f....
Let ?1 , ?2 , ... , ?? be independent, identically distributed random variables with p.d.f. ?(?) = ???−1, 0 ≤ ? ≤ 1 . c) Show that the maximum likelihood estimator for ? is biased, and find a function of the mle that is unbiased. (Hint: Show that the random variable −ln (??) is exponential, the sum of exponentials is Gamma, and the mean of 1/X for a gamma with parameters ? and ? is 1⁄(?(? − 1)).) d)...
Let X1, X2, . . . be a sequence of independent and identically distributed random variables...
Let X1, X2, . . . be a sequence of independent and identically distributed random variables where the distribution is given by the so-called zero-truncated Poisson distribution with probability mass function; P(X = x) = λx/ (x!(eλ − 1)), x = 1, 2, 3... Let N ∼ Binomial(n, 1−e^−λ ) be another random variable that is independent of the Xi ’s. 1) Show that Y = X1 +X2 + ... + XN has a Poisson distribution with mean nλ.
Let X1 and X2 be independent identically distributed random variables with pmf p(0) = 1/4, p(1)...
Let X1 and X2 be independent identically distributed random variables with pmf p(0) = 1/4, p(1) = 1/2, p(2) = 1/4 (a) What is the probability mass function (pmf) of X1 + X2? (b) What is the probability mass function (pmf) of X(2) = max{X1, X2}? (c) What is the MGF of X1? (d) What is the MGF of X1 + X2
Let X1 and X2 be independent identically distributed random variables with pmf p(0) = 1/4, p(1)...
Let X1 and X2 be independent identically distributed random variables with pmf p(0) = 1/4, p(1) = 1/2, p(2) = 1/4 (a) What is the probability mass function (pmf) of X1 + X2? (b) What is the probability mass function (pmf) of X(2) = max{X1, X2}? (c) What is the MGF of X1? (d) What is the MGF of X1 + X2? (Note: The formulas we did were for the continuous case, so they don’t directly apply here, but you...
A charity receives 2025 contributions. Contributions are assumed to be independent and identically distributed with mean...
A charity receives 2025 contributions. Contributions are assumed to be independent and identically distributed with mean 3125 and standard deviation 250. Calculate the probability that the total amount of contributions is greater than $6,320,000.   1. What do I know?   2. What do I want to find out? 3. What do we expect the answer to be? 4. How do I go from what I know to what I want to find? 5. Is the answer consistent with what I expected?  
You are given a number of i.i.d. (independent and identically distributed) observations that are (continuously) uniformly...
You are given a number of i.i.d. (independent and identically distributed) observations that are (continuously) uniformly distributed in the interval from X to X+10 , where X is an unknown real valued parameter. Derive the ML (maximum likelihood) estimator for X. Given the observations 16.10 , 22.84 , 19.96 , 24.54 , 15.36 , 19.01 , 15.65 , 24.20 , 14.63 , 22.33 , compute the ML estimate for X. If the ML estimate is a range of values, then...
You are given a number of i.i.d. (independent and identically distributed) observations that are (continuously) uniformly...
You are given a number of i.i.d. (independent and identically distributed) observations that are (continuously) uniformly distributed in the interval from X to X+7 , where X is an unknown real valued parameter. Derive the ML (maximum likelihood) estimator for X. Given the observations 28.91 , 26.52 , 28.54 , 28.69 , 26.86 , 23.90 , 26.08 , 26.73 , 25.65 , 25.14 , 29.51 , 26.77 , compute the ML estimate for X. If the ML estimate is a...
Losses covered by an insurance policy are uniform on [0, 2000]. An insurance company reimburses losses...
Losses covered by an insurance policy are uniform on [0, 2000]. An insurance company reimburses losses with a deductible of 700. Calculate the difference between the first quartile and the third quartile on the insurance company’s reimbursement.
Let ?1 and ?2 be two independent random variables with uniform distribution on [0, 1]. 1....
Let ?1 and ?2 be two independent random variables with uniform distribution on [0, 1]. 1. Write down the joint cumulative distribution function and joint probability density function of ?1 + ?2 and ?1?2
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT