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- 4)Suppose x is a random variable best described by a uniform probability distribution with a = 20and b = 40. Find P(x < 40). 5) Suppose x is a uniform random variable with a = 10 and b = 70. Find P(x > 34). 6)Suppose x is a random variable best described by a uniform probability distribution with a = 20and b = 40. Find P(x > 40)EXAMPLE 5a If the number of items produced in a factory during a week is a random variable with mean 100 and variance 400, compute an upper bound on the probability that this week's production will be at least 120.If we model the number of likes for a Facebook picture post as a Gaussian random variable with mean 2,000 and variance 90,000. Find the probability of getting less than 1,400 likes in terms of d. (a) Þ(2) (b) 1 – Þ(2) (c) ¢(2.5) (d) 1 – ¤(2.5)
- Suppose that40%of the applicants for a certain job possess advanced training in computerprogramming. Applicants are interviewed sequntially and are selected at random from the pool. Find theprobability that the 4th applicant with advanced training in programming is found on the 8th interview.To answer this question, first identify the random variable, its distribution and the parameter(s) of the distribution.Show that (1) the mean value of a weighted sum of random variables equals the weighted sum of the mean values and (2) the variance of a weighted sum of N random variables equals the weighted sum of all their covariances.At a toll-booth on-ramp there is a stochastic arrival distribution. Vehicles are counted in 20-second intervals, and vehicle counts are taken in 120 of these time intervals. Based on data collected, no vehicles arrived in 18 of the 120 count intervals. What is the number of the 120 intervals that 3 cars arrived?
- Suppose that we have disjoint normal populations A and B with equal population variances. Suppose we plan a sample of size 4 from from population A and a sample of size 9 from population B which we will pool to form the pooled variance. If you know the population variances are both in fact equal to 6, what is the probability that the pooled variance of the two samples will turn out to be less than 8 given your information?Suppose 500 people audition for admission to a dance school. Each dancer in one half of the group will be admitted with probability 0.07, while each dancer in the other half of the group will be admitted with probability 0.04. Let X be the total number of dancers admitted. (Notice that X is the sum of two binomial variables). (a) Find the mean and variance of X. (b) Use normal approximations to binomial random variables to approximate (i) the probability that more than 30 dancers are admitted. (ii) the probability that at least 20 dancers are admitted.List the values of the random variables defined in the following 4. The number of bounced checks (due to insufficient funds) that a bank receives in a day. 5. The number of Covid-19 patients that recovers from this sickness in a certain hospital per day.
- 5please send correct answer Q62 (a) Let Y be the random variable that counts the number of sixes which occur when a die is tossed 10 times. What type of random variable is Y? What is P (Y = 3), expected number of sixes,Var(Y )? (b) Let U be the random variable that counts the number of accidents that occur at an intersection in one week. What type of random variable is U? Suppose that, on average, 2 accidents occur per week. Find P(U = 2), E(U), and V ar(U). (c) Let X be the recorded body temperature of a healthy adult in degrees Fahrenheit. What type of rv is X? Estimate its mean and standard deviation, based on your knowledge of body temperatures.