Suppose that the waiting time X (in seconds) for the pedestrian signal at a particular street crossing is a random variable with the following pdf. · (1 − x/71)² 0 ≤ x < 71 {0 f(x) = {√ √ otherwise If you use this crossing every day for the next 6 days, what is the probability that you will wait for at least 10 seconds on exactly 2 of those days?
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- If a procedure meets all of the conditions of a binomial distribution except the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by P(x)equals=p left parenthesis 1 minus p right parenthesis Superscript x minus 1p(1−p)x−1 , where p is the probability of success on any one trial. Subjects are randomly selected for a health survey. The probability that someone is a universal donor (with group O and type Rh negative blood) is 0.15. Find the probability that the first subject to be a universal blood donor is the fifth person selected. The probability is ? (Round to four decimal places as needed.)Show that (X+1)/(n+2) is a biased estimator of the binomial parameter θ. Is this estimator asymptotically unbiased?If random variable x is exponentially-distributed with mean A =2, calculate P(X>3): 2 2e-2x x = 3 3 2 2e-2x X = 0 | 2e-2x dx | 3e-3*dx 2 3e-3x X = 2 .3 | 2e-2xdx
- Suppose that there are two assets that are available for investment and an investor has the following expected utility: EU = E(R,)– 0.5Ao, where expected return and standard deviation are expressed in decimals. For example, if expected return is 25%, standard deviation is 15%, and risk aversion is 5, expected utility is computed as: EU = 0.25 – 0.5×5x 0.15 = 0.1938 Now, assume that there is no other instrument (such as the risk-free security) available. Then, derive the analytical expressions for the optimal portfolio weights of the first and the second assets for this specific investor. (Hint: We are not talking about a numerical response here. Rather, you are asked to derive mathematically how you would compute for the optimal portfolio.)Suppose that the waiting time X (in seconds) for the pedestrian signal at a particular street crossing is a random variable with the following pdf. f(x) = {1 ; (1 − x/68)³ 0 ≤ x < 68 otherwise If you use this crossing every day for the next 10 days, what is the probability that you will wait for at least 10 seconds on exactly 4 of those days?A school committee with four members is to be chosen randomly from a group consisting of 6 men and 5 womenLet X be the number of men in the committee.What is E(X)?
- How were the correct answers of 0.1251 and 0.0313 attained?As soon as one components fails, the entire system will fail. Suppose each component has a lifetime that is exponentially distributed with ? = 0.01 and that components fail independently of one another. Define events Ai = {ith component lasts at least t hours}, i = 1, . . . , 5, so that the Ais are independent events. Let X = the time at which the system fails—that is, the shortest (minimum) lifetime among the five components. P(X ≥ t)? F(t) = P(X ≤ t)? the pdf of X?Samples of rejuvenated mitochondria are mutated (defective) in 10% of cases. Suppose a study needs to have 5 mutated samples, and they keep testing samples until they get the desired number. Assume the samples are independent for the mutation, let X denote the number of not mutated samples being tested until 5 mutated samples are found, (a) Find P(X=20) [Select] (b) Find E(X) [Select] (c) Find V(X) [Select]
- You want the probability that an attacker without particular information must be able to crack your password on the first attempt to be at most where n=59. Also, assume that the password consists only of small letters from the English alphabet (26 letters) and the numbers 0-9. How long must your password be? 1 2n,Suppose 1.8% of every Filipino births result in twins. From a random sample of 1000 births, let X be the number of twins. That is X = {0, 1, 2, ..., 1000). Find the E(X).Suppose that approximately 40% of the population has Type O+ blood. You take a sample of 5 persons. Let Y denote the number of persons in the sample with Type O+ blood. Find each of the following. (a) Pr{Y = 2} = (b) Pr{Y < 2} = (c) Pr{Y ≥ 2} =