A test of n circuits such that each circuit is acceptable with probability p, independent of...
A test of n circuits such that each circuit is acceptable with probability p, independent of the outcome of any other test. Find the joint PMF of X, the number of acceptable circuits, and Y, the number of acceptable circuits found before observing the first reject.
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A test of n circuits such that each circuit is acceptable with
probability p, independent of...
3. You are testing two integrated circuits. In each test you either accept (designate by A) or re...
3. You are testing two integrated circuits. In each test you either accept (designate by A) or reject (designate by R), with probabilities of 0.9 and 0.1 respectively. Define x-# of acceptable ICs # of tests before you get the first reject. a. Find the joint PMF of X and Y. Also find the Marginal PMFs of each R.V. Are X and Y independent? b. What is the Probability that X is equal to Y? c. Find the Joint Expectation...
Problem 1 Consider a sequence of n+m independent Bernoulli trials with probability of success p in each trial. Let N be the number of successes in the first n trials and let M be the number of suc...
Problem 1 Consider a sequence of n+m independent Bernoulli trials with probability of success p in each trial. Let N be the number of successes in the first n trials and let M be the number of successes in the remaining m trials. (a) Find the joint PMF of N and M, and the marginal PMFs of N and AM (b) Find the PMF for the total number of successes in the n +m trials.
Problem 1 Consider a sequence...
You perform a sequence of m+n independent Bernoulli trials with success probability p between (0, 1)....
You perform a sequence of m+n independent Bernoulli trials with success probability p between (0, 1). Let X denote the number of successes in the first m trials and Y be the number of successes in the last n trials. Find f(x|z) = P(X = x|X + Y = z). Show that this function of x, which will not depend on p, is a pmf in x with integer values in [max(0, z - n), min(z,m)]. Hint: the intersection of...
3a. On a certain aircraft, the main control circuit on an autopilot fails with probability p....
3a. On a certain aircraft, the main control circuit on an autopilot fails with probability p. A redundant backup eircuit fails independently with probability q. The aircraft can fly if at least one of the circuits is functioning. Find the probability that the aircraft cannot fly. 4 pt. b. Let X and Y be the random variables with respective pmf's shown in the side figure. Compute var(X), var(Y). 23 pt. 3 pt. c. | At Problem 3-b, find the PMF...
Wiout feplacement. 6.9 Consider a sequence of Bernoulli trials with success probability p. Let X denote the number of t...
Wiout feplacement. 6.9 Consider a sequence of Bernoulli trials with success probability p. Let X denote the number of trials up to and including the first success and let Y denote the number of trials up to and including the second success. a) Identify the (marginal) PMF of X c) Determine the joint PMF of X and Y. d) Use Proposition 6.2 on page 263 and the result of part (c) to obtain the marginal PMFS of X and Y....
(Yates 1.2.2) An integrated circuit factory has three machines X,Y, and Z. Test one integrated circuit produced by each...
(Yates 1.2.2) An integrated circuit factory has three machines X,Y, and Z. Test one integrated circuit produced by each machine. Either a circuit is acceptable (a) or it fails (f). An observation is a sequence of three test results corresponding to the circuits from machine X,Y, and Z, respectively. For example, aaf is the observation that the circuits from X and Y pass the test and the circuit from Z fails the test (a) What are the elements of the...
[20] A plant sheds X seeds, where X B(n,p).Each seed germinates with probability o independently of...
[20] A plant sheds X seeds, where X B(n,p).Each seed germinates with probability o independently of all others. Let Y number of seedlings. 5. a) Find the pmf of Y b) Determine E(Y) and Var(Y).
The number of balls in a box, N, is a Poisson variable with rate A. Each ball in the box can be white with probability p or red, with probability q = 1-p. Let X be the number of white balls in a box...
The number of balls in a box, N, is a Poisson variable with rate A. Each ball in the box can be white with probability p or red, with probability q = 1-p. Let X be the number of white balls in a box and Y the number of red balls in the same box, so that X+Y = N. The joint probability P(X i, Y = j), i, j 0? (b (A)
The number of balls in a box,...
Suppose X and Y are independent Binomial random variables, each with n=3 and p=9/10. a. Find...
Suppose X and Y are independent Binomial random variables, each with n=3 and p=9/10. a. Find the probability that X and Y are equal, i.e., find P(X=Y). b. Find the probability that X is strictly larger than Y, i.e., find P(X>Y). c. Find the probability that Y is strictly larger than X, i.e., find P(Y>X).
5. A series of independent Bernoulli(p) trials is performed, labeled 1,2,3,...Let X be the location (label)...
5. A series of independent Bernoulli(p) trials is performed, labeled 1,2,3,...Let X be the location (label) of the first success observed, and Y be the location of the second success observed. (a) Find the joint PMF of X and Y; give your result as a general formula. (It may help to start by considering specific sequences, such as "001001", where X 3 and 6 (b) Write out thefirst of your PMF in table format, covering the range 1 sX 4,13YS...
3. You are testing two integrated circuits. In each test you either accept (designate by A) or reject (designate by R), with probabilities of 0.9 and 0.1 respectively. Define x-# of acceptable ICs # of tests before you get the first reject. a. Find the joint PMF of X and Y. Also find the Marginal PMFs of each R.V. Are X and Y independent? b. What is the Probability that X is equal to Y? c. Find the Joint Expectation...
Problem 1 Consider a sequence of n+m independent Bernoulli trials with probability of success p in each trial. Let N be the number of successes in the first n trials and let M be the number of successes in the remaining m trials. (a) Find the joint PMF of N and M, and the marginal PMFs of N and AM (b) Find the PMF for the total number of successes in the n +m trials.
Problem 1 Consider a sequence...
3a. On a certain aircraft, the main control circuit on an autopilot fails with probability p. A redundant backup eircuit fails independently with probability q. The aircraft can fly if at least one of the circuits is functioning. Find the probability that the aircraft cannot fly. 4 pt. b. Let X and Y be the random variables with respective pmf's shown in the side figure. Compute var(X), var(Y). 23 pt. 3 pt. c. | At Problem 3-b, find the PMF...
Wiout feplacement. 6.9 Consider a sequence of Bernoulli trials with success probability p. Let X denote the number of trials up to and including the first success and let Y denote the number of trials up to and including the second success. a) Identify the (marginal) PMF of X c) Determine the joint PMF of X and Y. d) Use Proposition 6.2 on page 263 and the result of part (c) to obtain the marginal PMFS of X and Y....
(Yates 1.2.2) An integrated circuit factory has three machines X,Y, and Z. Test one integrated circuit produced by each machine. Either a circuit is acceptable (a) or it fails (f). An observation is a sequence of three test results corresponding to the circuits from machine X,Y, and Z, respectively. For example, aaf is the observation that the circuits from X and Y pass the test and the circuit from Z fails the test (a) What are the elements of the...
[20] A plant sheds X seeds, where X B(n,p).Each seed germinates with probability o independently of all others. Let Y number of seedlings. 5. a) Find the pmf of Y b) Determine E(Y) and Var(Y).
The number of balls in a box, N, is a Poisson variable with rate A. Each ball in the box can be white with probability p or red, with probability q = 1-p. Let X be the number of white balls in a box and Y the number of red balls in the same box, so that X+Y = N. The joint probability P(X i, Y = j), i, j 0? (b (A)
The number of balls in a box,...
5. A series of independent Bernoulli(p) trials is performed, labeled 1,2,3,...Let X be the location (label) of the first success observed, and Y be the location of the second success observed. (a) Find the joint PMF of X and Y; give your result as a general formula. (It may help to start by considering specific sequences, such as "001001", where X 3 and 6 (b) Write out thefirst of your PMF in table format, covering the range 1 sX 4,13YS...
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