Compute the following probabilities: P(X+Y > 3) P(XY = 2) = P( > 1) =|
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- assume that Pr[A] = 0.45, Pr[B] = 0.35, and Pr[A n B] = 0.25. Compute the following conditional probabilities: (1) Pr[A|B] = (2) Pr[B|A] =1. Answer the following questions using the probability tree below: .2 .3 X .3 .8 a Y (a) What is the value of z? (b) What is the probability of X occurring? (c) What is Pr[Xa] (Note: Pr[Xa] = Pr[X and a].) (d) What is Pr[X_or a]? (e) What is Pr[a|X]? (f) What is Pr[c]?Rohan appeared in a job interview for the position of a Portfolio Analyst. The interviewer asked jim - Assume that a group of securities has the following characteristics:(a) the standard deviation of each security is equal to σA ; (b) covariance of returns σ AB is equal for each pair of securities in the group. What is the variance of a portfolio containing six securities which are equally weighted?
- A branch of a certain bank has six ATMs. Let X represent the number of machines in use at a particular time of day. The cdf of X is as follows: F(X) = (b) Calculate the following probabilities directly from the cdf: (a) p(2), that is, P(X = 2) (c) 0 x 3) P(2 ≤x≤5) P(2 < X <5)The probability function of the amount of soft drink in a can is f(x)=4cx for11.5 <X< 12.5 oz. Determine the value of c such that f(x) represents a p.d.f..Then, find the following probabilities:(a) P(X > 11.5), (b) P(X < 12.25), and (c) P(11.75 <X< 12.25).The profits of a mobile company are normally distributed with Mean of R.O (180) and standard deviatic of R.O (8). a. Find the probability that a randomly selected mobile has a profit greaterthan R.O ( 190). b. Any mobile phone which profit is greater than R.O (190) is defined as expensive. Find the probability that a randomly selected mobile has aprofit greaterthan R.O ( (200) given that it is expensive. Half of expensivemobile phones have aprofit greaterthan R.O h. Find the value of h. C.
- Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using the table. Probabilities of Girls x(girls) P(x) x(girls)| P(x) |x(girls)| P(x) 0.000 0.122 10 0.061 1 0.001 0.183 11 0.022 2 0.006 7 0.210 12 0.006 3 0.022 8 0.183 13 0.001 4 0.061 9 0.122 14 0.000 Find the probability of selecting 12 or more girls. 0.001 O 0.022 0.006 O 0.007Let X represent the number of homes a real estate agent sells during a given month. Based on previous sales records, she estimates that P(0)= 0.62, P(1)= 0.21, P(2)= 0.13, P(3)= 0.03, P(4)= 0.01, with negligible probability for higher values of x. Find the long-term average number of homes the real estate agent expects to sell each month.Calculate the following probabilities in two decimal places: (a) Y is distributed x 1. Then, Pr( Y>9.49) = (b) Y is distributed to. Then, Pr( Y> -0.5) = (c) Y is distributed F4,- Then, Pr( Y 696 or Y<304) =
- Of 9 randomly selected male students, Xj used Apple computer, whereas of 12 randomly selected female student, X2 used Apple computer. Let: p1 and p2 denote the probabilities that a randomly selected male and female students, respectively, played tennis. what is unbiased estimator of P1 - P2 ? X2 Da. 7+ 12 X1 X2 Ob. 49 144 X2 12 X1 Od. 49 X2 144Find the probabilities or area of P(0<z<1.65).(b) Let X~N(40,144) and if Y = 2X – 1 Find the following probabilities: (i) P(X 50) (iii)P(35 < X < 45),(iv)P(-45 < Y < 45).(v)P(-50 < Y < 100)