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- Suppose the probability of erroneously transmitting a single digit is P=0.03. Compute the probability of transmitting a 4-bit code word with (a) at most one error, and (b) exactly four errors.The event that exactly one of the events A or B occurs can be represented as (A intersection B') U (A' intersection B). Show that P[(A intersection B') U (A' intersection B)] = P(A)+P(B) - 2P(A intersection B)Inside of a jar are four balls that are labeled 1, 2, 3, and 4. You randomly choose three balls from the jar (w/ replacement). Let X = smallest of the three numbers on the balls selected (i) What is the pmf for X? (ii) What is the CDF for X? (iii) What is P(X<3)?
- = 4. Consider 3 events A, B and C with Pr(A) = a, Pr(B) = 3a, Pr(C) = 5a, and Pr(An B) = Pr(ANC) = Pr(BC) = 28. Prove that ß ≤ 11. 14Let A₁-(2, 4, 6, ....., 2i} where i = 1, 2, 3, ... ex A7 (2.4.6.8.10.12.143 1) Find A F4 {2,4,.., 2n-3} % F5 B {2,4,.., 2n-2} O UA, Il app.honorlock.com is sharing your screen. Stop sharing Hide A F6 O C {2,4,.., 2n-1} D {2,4,..., 2n} F7 PrtScn F8 Calculator Home F9 W Guidel End O F10Many people believe that the daily change in price of a company's stock in the stock market is a random variable with mean 0 and variance o² during the middle 2 months between 2 earning report dates when there is not much news released. That is, if Yn represents the closing price of the stock on the nth trading day of that period, then Yn = Yn-1+Xn, for 1 ≤ n ≤ 60, where X₁, X2,..., X60 are independent and identically distributed random variables with mean 0 and variance o². Suppose that the stock price at the beginning of the 2-month period is 100. If o = 2, what is the approximate probability that the stock's closing price on the 30th trading day will exceed 110, i.e., what is P(Y30 > 110)
- Supposed that n students are selected at random without replacement from a class containing T students, of whom A are boys & T - A are girls. Let x denote the number of boys that are obtained. For what sample size n will Var(X) be a maximum?Suppose that one variable, x, is chosen randomly and uniformly from [0, 2], and another variable, y, is also chosen randomly and uniformly from [0, 4]. What is the probability that x≤y≤2x+1?The probability for x≤y≤2x+1 is2. It is estimated that 10% of the vehicles entering Canada from the United States carry undeclared goods. Use the normal approximation to calculate the probability that a search of 500 randomly selected vehicles will find fewer than 50 with undeclared goods. Use continuity correction.
- 1. Suppose that an urn contains 8 red balls and 4 white balls. We draw 2 balls from theurn without replacement, (a) If we assume that at each draw, each ball in the urn isequally likely to be chosen, what is the probability that both balls drawn are red? (b)Now suppose that the balls have different weights, with each red ball having weight rand each white ball having weight w. Suppose that the probability that a given ball inthe urn is the next one selected is its weight divided by the sum of the weights of allballs currently in the urn. Now what is the probability that both balls are red? 2. Consider the following game played with an ordinary deck of 52 playing cards: Thecards are shuffled and then turned over one at a time. At any time, the player canguess that the next card to be turned over will be the ace of spades; if it is, then theplayer wins. In addition, the player is said to win if the ace of spades has not yetappeared when only one card remains and no guess has yet been…Suppose the distribution of some random variable X is modeled as Negative binomial with parameters, p and r, where p is the probability of success and r is the total number of success over the trials. Find the method of moment (MM) estimators for (p,r), in closed algebraic form expressions based on a random sample of size n, X1, X2,...,Xn.1. Let X ~ Poisson(A) and Y ~ Poisson(u). Assume that X and Y are independent. Use probability generating functions to find the distribu- tion of X + Y.
