Suppose that daily log-returns are N(0.0005,0.012). Find the smallest value of t such that P(P/Po 2...
Question He Find the present value Po of the amount P = $100,000 due t= 5 years in the future and invested at interest rate k=8%, compounded continuous The present value of $100,000 is $ (Round to the nearest cent as needed.)
5. Consider a binomial tree model for a stock price, S(n) as above. Find a probability value p, in the case when the risk free assest has a continuous compounding rate of r. What are the bounds on e', that is, what is the smallest and largest value it can be in terms of u and d which prevent arbitrage? S(n) is a stock price where K1)u with probability p and K(1d with probability 1-p and K(1). K(n) are independent...
(1) Suppose the pdf of a random variable X is 0, otherwise. (a) Find P(2 < X < 3). (b) Find P(X < 1). (e) Find t such that P(X <t) = (d) After the value of X has been observed, let y be the integer closest to X. Find the PMF of the random variable y U (2) Suppose for constants n E R and c > 0, we have the function cr" ifa > 1 0, otherwise (a)...
random variable T has a t-distribution with 7 degree of freedom. Find P(-1<= T<=1). Suppose P(T<=C=0.9, what is the value of C?
Suppose that the probability that Sally eats ice cream for dessert is p, and the probability that she eats cake is r = 1 – p. Let P_n be the probability that in n days, there are never two days in a row that Sally's had cake for desert. a) Find P_2 and P_3 . b) By conditioning on the outcome of the first day's dessert, find a recursive formula for P_n in terns of P_{n-1} and P_{n-2} . c)...
1) Suppose that X ∼ N(0,1) find: P(X<=1.36) Round your answer to the nearest thousandth. 2) Suppose that X ∼ N(0,1) find: P(|X-0.9|>=1.35) Round your answer to the nearest thousandth. 3)Suppose that X ∼ B(8, 0.25). Calculate p(X=1) Round your answer to the nearest thousandth. 4) Suppose that X ∼ B(10, 0.23). Calculate P(X ≥ 7) Round your answer to the nearest thousandth. 5)Suppose that X ∼ U(-5, 10). Find the P(-2 ≤ X ≤ 5) Round your answer to...
4. Suppose T (n) satisfies the recurrence equations T(n) = 2 * T( n/2 ) + 6 * n, n 2 We want to prove that T (n)-o(n * log(n)) T(1) = 3 (log (n) is log2 (n) here and throughout ). a. compute values in this table for T (n) and n*log (n) (see problem #7) T(n) | C | n * log(n) 2 4 6 b. based on the values in (a) find suitable "order constants" C and...
Plese use R-Studio to answer this question. qbinom(p, size, prob) gives the smallest x value so that the probability of being less than or equal to x is at least p. Try the following: pbinom(0:10, size=10, prob=0.5) ; qbinom(0.75, size=10, prob=0.5) What is the value for which 90 percent of the probability is smaller than it, when you flip a fair coin 20 times?
4. Suppose that N is a random variable having a conditional Poisson distribution with ability mass function prob- 1 (log 3) PN(i) i 1,2,3,... 2 i (a) Show that the mean of N is 3 log 3 1.6479, 2 and the variance of N is 3(log 3)2 3 log 3 0.7427. 2 4 (b) Calculate the probability P(N -4I 20). (c) Use the Bienaymé-Chebyshev inequality to give a lower bound for the probability that N takes values within 2 standard...
A.) for a binomial distribution with p= 0.65, find the smallest value of n so that the normal distribution is a reasonable approximation to the binomial distribution. N=? B.) given the Bernoulli experiment with n=60 and p= 0.6, use the normal distribution to estimate the following (round answers to four decimal places) P(x=40) P(x=28) P(x=32) C.) given the Bernoulli experiment with n= 12 and p= 0.5, use the normal distribution to estimate the following (round to four decimal places) P(4...