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In Exercises 1–8, use Bayes’ theorem or a tree diagram to calculate the indicated probability. Round all answers to four decimal places. [HinT: See Quick Example 1 and Example 3.]
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- Section 2 7. The joint probability function for X and Y is given below. Find Pr(X >Y). fx,x (x, y) 0.24 0.36 1 0.21 0.19 0.79 0.43 None of the given options. 0.21 0.57arrow_forwardPart 2 of 2 What is the probability that a randomly chosen senior will have a GPA greater than 4.1? The probability that a randomly chosen senior will have a GPA greater than 4.1 is X Sarrow_forwardYou are playing a game at a carnival. You can win $5 with probability 0.15 on each round, but if you lose, you pay $2. Assume each round that you play is independent of the others. Let X be the number of rounds it takes for you to get your first win (including the first win). X is distributed [ Select ] The expectation of X is [Select ] If you stop playing after your first win, your expected winnings (i.e. net profit, or the number of dollars you win or lose from playing the game; positive if you win more money than you lose) is [ Select ] You are playing a game at a carnival. You can win $5 with probability 0.15 on each round, but if you lose, you pay $2. Assume each round that you play is independent of the others. Let X be the number of rounds it takes for you to get your first win (including the first win). X is distributed [ Select ] [ Select ] The expectation of X Geometric(p = 0.15) Exponential(\lambda = 0.15) If you stop playing aft number of dollars you winnings (i.e. net…arrow_forward
- Events A and B are independent with P(AB) = 0.2 and P(A'B) = 0.6. 3a. Find P(B).arrow_forwardCalculate the relative frequency P(E) using the given information. Six hundred adults are polled, and 480 of them support universal health-care coverage. E is the event that an adult supports universal health-care coverage. HINT [See Example 1.] P(E) = =arrow_forwardTask 2. Provide a proof of Theorem 3.3 part a. 106 Probability and Statistics with R Theorem 3.3 If a and b are real-valued constants, then (1) Mx+a(t) = E [e*+a)*] = eat . Mx(t).arrow_forward
- %A. l. https://docs.google.com/fo YO 4.4 O 3.96 O 1.8 نقطة واحدة Let X denote the number of colleges where you will apply after your results and P(X =x) denotes your probability of getting admission in x number of colleges. It is given that if x = 0 or 1 if x = 2 if x 3 or 4 otherwise kx, 2kx, P(X = x) 3= %3D k(5 - x), 0, Where k is a positive constant. Then the probability that you will get admission in at most 2 colleges is 0.625arrow_forwardWhat do the functions Y. YY look like? Are there any maximum or 1+1 minimum probability at any particular angle(s) for these functions? [You don't have to prove this mathematically if you can provide your reasoning clearly.]arrow_forwardSection 1 4. The continuous random variable X has the following probability density function S{(1+æ), 0< x < 2; 0, fx (x) otherwise. The median, m, of a continuous random variable Y satisfies Pr(Y < m) = 0.5. Find the median of X. (Choose the option closest to the answer.) 0.8 1.4 1.2 1.6 1.0 Save For Later Nextarrow_forward
- (Sec. 3.2) A student is required to enroll in one, two, three, four, five, six on the desired courseload) at a local university. Let Y the number of classes the next student enrolls themselves in. The probability that y classes are selected is known to be proportional to y+1, in other words the pmf of Y is given by p(y) = k(y+1) for y 1,...,7, and 0 otherwise (a) What is the value of k? or seven classes (depending (b) What is the probability that at most four classes are enrolled in? (c) What is the probability that a student enrolls in between three and five classes (inclusive)? y? /40 for y 1,.,7 be the pmf of Y? Explain why why not (d) Could p(y) orarrow_forwardcalculate the relative frequency P(E) using the given information. Five hundred adults are polled, and 350 of them support universal health-care coverage. E is the event that an adult supports universal health-care coverage. HINT [See Example 1.] P(E) =arrow_forwardQ. 3 The resistance of an electrical component follows a pdf given by What is the probability that the resistance is less than 27.arrow_forward
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