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- The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200 minutes, with the results shown in the table below. Complete (a) through (c) to the right. Frequency D Arrivals 0 12345678 RRESHKAN 23 50 40 35 21 MOY a. Compute the expected number of arrivals per minute. μ= (Type an integer or decimal rounded to three decimal places as needed.) b. Compute the standard deviation. O= (Type an integer or decimal rounded to three decimal places as needed.) c. What is the probability that there will be fewer than 2 arrivals in a given minute? P(x<2)= (Type an integer or decimal rounded to three decimal places as needed.)Assume the lifetime of electronic systems T (based on months) has Exponential distribution with λ=0.01. We select a random sample of 5 systems (random lifetime of these systems are T1, T2, T3, T4, and T5). Assume, S= T1+T2+ T3+ T4+ T5. a. Find E[S] . b. Find Standard Deviation of S (σSσS). c. Find median of T1.A coin weighted so that P(H) = % and P(T) = g is tossed four times. Let X is a random variable which denotes the longest string of tails which occurs. Find the distribution, expectation, variance and standard deviation of X’
- The expected value of this estimator is ?Answer the picture below with the given formula of Standard deviationLet i, denote the effective annual return achieved on an equity fund achieved between time (t-1) and time t. Annual log-returns on the fund, denoted by In(1+i), are assumed to form a series of independent and identically distributed Normal random variables with parameters u = 6% and σ = 14%. An investor has a liability of £10,000 payable at time 15. Calculate the amount of money that should be invested now so that the probability that the investor will be unable to meet the liability as it falls due is only 5%.
- According to records, the amount of precipitation in a certain city on a November day has a mean of 0.10 inc 0.06 inches. What is the probability that the mean daily precipitation will be 0.11 inches or less for a random sample of 4 many years)? Carry your intermediate computations to at least four decimal places. Round your answer to at least three de 0 X6.2/37.54 A random variable is Poisson distributed with A = 0.50 arrivals per minute. For the corresponding exponential distribution, and x = minutes until the next arrival, identify the mean of x and determine the following: a. P(x S 0.5) b. P(x S1.5) с. Р\х 2.5) d. P(x 3.0)
- 4) Computing the standard deviation ơ, of N measurements y,,y1,...yy of a singles quantity y requires that you compute the sum (y, - j). Prove that this sum can be rewritten as i=1 N i=1 i=1 This problem is a good exercise using summation notation. Many calculators use the expression on the right to compute the standard deviation. Can you determine why?Suppose that po = 25% of a population has a certain characteristic and that a random sample of size n=300 is taken. Determine the probability that more than x = 84 people in the sample have the characteristic. i.e. calculate P(p > 84/300) = P(p > 0.28) . Enter your answer to 3 decimal places. Hint: You will need the normal table and use the formula p – Po N(0, 1) Po(1-po)solve all 6 to 8