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Problem 1 Version 1 1. An engineer is going to install a number of switches in...
1. there is a drawer with 6 blue socks and 4 white socks. someone picks 2...
1. there is a drawer with 6 blue socks and 4 white socks. someone picks 2 socks at random. What’s the probability that its a matching pair of socks? 2. Suppose that in a certain country, 10% of the elderly people have diabetes. It is also known that 30% of the elderly people are living below poverty level, and 35% of the elderly population falls into at least one of these categories. A. What proportion of elderly people in this...
random probability course Problem 1: [60 points) A discrete random variable has the following probability mass...
random probability course
Problem 1: [60 points) A discrete random variable has the following probability mass function 2s+ 1,2,3 Find: (a) P(x <2) (b) P(l s X<3) (c) E(x) (d) Ea/x) Problem 2: [40 points] Calls to an airline reservation system have a probability of 0.7 of connecting successfully (i.e., not obtaining a busy tone). Assume that 8 independent calls are placed to the airline. (a) What is the probability that at least one call will connect successfully? (b) What...
1. In this problem, you are going to numerically verify that the Central Limit Theorem is valid e...
1. In this problem, you are going to numerically verify that the Central Limit Theorem is valid even when sampling from non-normal distributions. Suppose that a component has a probability of failure described by a Weibull distri- bution. Let X be the random variable that denotes time until failure; its probability density is: for a 2 0, and zero elsewhere. In this problem, assume k 1.5, 100 a) Simulate drawing a set of N-20 sample values, repeated over M 200...
There are N sites that need protection (number them 1 to N). Someone is going to pick one of them to attack, and you must pick one to protect. Suppose that the attacker is going to attack site i with probability qi. You plan on selecting a site to protect
There are N sites that need protection (number them 1 to N). Someone is going to pick one of them to attack, and you must pick one to protect. Suppose that the attacker is going to attack site i with probability qi. You plan on selecting a site to protect, with probability pi of selecting site i. If you select the same site to protect that the attacker chooses to attack, you successfully defend that site. The choice of {qi}...
1 point) It is known that a certain lacrosse goalie will successfully make a save 89...
1 point) It is known that a certain lacrosse goalie will successfully make a save 89 84% of the time. Suppose that the lacrosse goalie attempts to make 13 saves. What is the probability that the lacrosse goalie will make at least 10 saves? Let X be the random variable which denotes the number of saves that are made by the lacrosse goalie. Find the expected value and standard deviation of the random variable E(X) Note: you can find special...
[20 points] Problem 2 - Monte Carlo Estimation of Definite Integrals One really cool application of...
[20 points] Problem 2 - Monte Carlo Estimation of Definite Integrals One really cool application of random variables is using them to approximate integrals/area under a curve. This method of approximating integrals is used frequently in computational science to approximate really difficult integrals that we never want to do by hand. In this exercise you'll figure out how we can do this in practice and test your method on a relatively simple integral. Part A. Let X be a random...
Problem 2 (25 Points) Monitor comestive phone call going through a tation on the intersection of...
Problem 2 (25 Points) Monitor comestive phone call going through a tation on the intersection of Delt-line Road and Preston Roul Clay chall un either a voice call (if is speaking or a data call of the call is c rying non-voice signal). Note that C- 1 if call. voice, otherwise -0. Voice and data callo arrive with probability p and I-P, respectively. Now consider a random Variable Nowhere N G + ... + is the number of voice calles...
1. In this problem, we are going to look at a three-level system. A spin-1 particld is placed in ...
1. In this problem, we are going to look at a three-level system. A spin-1 particld is placed in a constant magnetic field along the a-direction with strength B,. The spin-1 particle İs initialized in a z-eigenstate with positive eigenvalue h, ie, the i 1,m 1) state. What is the probability to find the negative eigenvalue the spin along the z axis as a function of time? Assume that the spin-1 particle has inagnetic moment 2 × μιι, i.e. that...
1. In a taste test of Pepsi vs Coke, suppose 55% of tasters cannot correctly identify which cola ...
1. In a taste test of Pepsi vs Coke, suppose 55% of tasters cannot correctly identify which cola they are drinking. Suppose that 6 tasters participate in a test by drinking. Random variable X represents the number of tasters who succeed. Draw the probability mass function (PMF). (3 pts) Note 1: For histogram, provide a bar at each of z. Note 2: For histogram, be sure to mark the height of each bar. Hint: Choosing k out of n, there...
random probability course
Problem 1: [60 points) A discrete random variable has the following probability mass function 2s+ 1,2,3 Find: (a) P(x <2) (b) P(l s X<3) (c) E(x) (d) Ea/x) Problem 2: [40 points] Calls to an airline reservation system have a probability of 0.7 of connecting successfully (i.e., not obtaining a busy tone). Assume that 8 independent calls are placed to the airline. (a) What is the probability that at least one call will connect successfully? (b) What...
1. In this problem, you are going to numerically verify that the Central Limit Theorem is valid even when sampling from non-normal distributions. Suppose that a component has a probability of failure described by a Weibull distri- bution. Let X be the random variable that denotes time until failure; its probability density is: for a 2 0, and zero elsewhere. In this problem, assume k 1.5, 100 a) Simulate drawing a set of N-20 sample values, repeated over M 200...
1 point) It is known that a certain lacrosse goalie will successfully make a save 89 84% of the time. Suppose that the lacrosse goalie attempts to make 13 saves. What is the probability that the lacrosse goalie will make at least 10 saves? Let X be the random variable which denotes the number of saves that are made by the lacrosse goalie. Find the expected value and standard deviation of the random variable E(X) Note: you can find special...
[20 points] Problem 2 - Monte Carlo Estimation of Definite Integrals One really cool application of random variables is using them to approximate integrals/area under a curve. This method of approximating integrals is used frequently in computational science to approximate really difficult integrals that we never want to do by hand. In this exercise you'll figure out how we can do this in practice and test your method on a relatively simple integral. Part A. Let X be a random...
Problem 2 (25 Points) Monitor comestive phone call going through a tation on the intersection of Delt-line Road and Preston Roul Clay chall un either a voice call (if is speaking or a data call of the call is c rying non-voice signal). Note that C- 1 if call. voice, otherwise -0. Voice and data callo arrive with probability p and I-P, respectively. Now consider a random Variable Nowhere N G + ... + is the number of voice calles...
1. In this problem, we are going to look at a three-level system. A spin-1 particld is placed in a constant magnetic field along the a-direction with strength B,. The spin-1 particle İs initialized in a z-eigenstate with positive eigenvalue h, ie, the i 1,m 1) state. What is the probability to find the negative eigenvalue the spin along the z axis as a function of time? Assume that the spin-1 particle has inagnetic moment 2 × μιι, i.e. that...
1. In a taste test of Pepsi vs Coke, suppose 55% of tasters cannot correctly identify which cola they are drinking. Suppose that 6 tasters participate in a test by drinking. Random variable X represents the number of tasters who succeed. Draw the probability mass function (PMF). (3 pts) Note 1: For histogram, provide a bar at each of z. Note 2: For histogram, be sure to mark the height of each bar. Hint: Choosing k out of n, there...
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Question 501 pts
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