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- A delivery truck travels from point A to point B and back using the same route each day. There are four traffic lights on the route. Let X1 denote the number of red lights the truck encounters going from A to B and X2 denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (X1, X2) is given by Please show complete solution.The battery life of a mobile device is uniformly distributed between 9 to 12 hours. Find the probability that the battery life will be between 10.5 and 11.5 hours.There are two boxes. In each box there are 4 cards with a different number printed on it. The four cards have been numbered as 1,2,3,4 in each box. Two cards are drawn random from each box. The random variable X represents the difference between the number on the card from box 1 minus the number on the card from box 2.a) Find the mean of this probability distribution. (i.e. Find E[X] )b) Find the variance and standard deviation of this probability distribution.(i.e. Find V[X] and SD[X])The random variables M and W are defined as follows:M = X+5 and W = (1/2)X+5c) Find E[M] and E[W].d) Find V[M] and V[W].e) Mary and William play a game using the cards in the above boxes. Randomly two cards are drawn, and Mary records his score using the random variable M and William uses the random variable W. They repeat this for a large number of times and compare their scores. Comment on any likely differences or similarities of their scores.
- Two tetrahedral dice, each with faces labelled 1, 2, 3 and 4, are thrown and the random variable X represents the sum of the numbers shown on the dice. li) Find the probability distribution of X. (ii) Illustrate the distribution and describe the shape of the distribution. (iii) What is the probability that any throw of the dice results in a value of X which is an odd number?Assume that when adults with smartphones are randomly selected, 38% use them in meetings or classes. If 25 adult smartphone users are randomly selected, find the probability that exactly 16 of them use their smartphones in meetings or classes. The probability is (Round to four decimal places as needed.) ry nsplease send handwritten solution
- The time between busses on Stevens Creek Blvd is 12 minutes. Therefore the wait time of a passenger who arrives randomly at a bus stop is uniformly distributed between 0 and 12 minutes. Find the probability that a person randomly arriving at the bus stop to wait for the bus has a wait time of at most 5 minutes.The table summarizes results from 988 pedestrian deaths that were caused by automobile accidents. Pedestrian Deaths DriverIntoxicated? Pedestrian Intoxicated? Yes No Yes 48 77 No 217 646 If one of the pedestrian deaths is randomly selected, find the probability that both the pedestrian and the driver were intoxicated. Please enter a decimal to 4 places.Probability =Faults occur on a piece of string at an average rate of one every three metres. Bobbins, each containing 5 metres of this string are to be used. What is the probability that a randomly selected bobbin will contain (a) two faults. (b) at least two faults.
- The probability of Pakistan to win a KABBADI match against India is 0.9117. Both teams played a series of 7 Matches, Find probability that Pakistan wins 1. exactly 4 matches 2. at most 2 matches 3. at least 5 matchesMAN Assume that when human resource managers are randomly selected, 62% say job applicants should follow up within two weeks. If 7 human resource managers are randomly selected, find the probability that exactly 4 of them say job applicants should follow up within two weeks. The probability is (Round to four decimal places as needed.)Giving a test to a group of students, the grades and gender are summarized below Grades vs. Gender А В C Male 5 16 13 Female 15 8. If one student was chosen at random, find the probability that the student got a B. Probability (Round to 4 decimal places)