Probability and Statistics- Mathematics Solved Homework Sample



Show enough of your work so that I will be able to tell how you arrived at your answers.

  1. Consider the probability distribution below.

x P(x)

10 0.1

20 0.2

30 0.3

40 0.3

50 0.1

  1. Calculate the probability that a randomly selected value of X will be less than 36.
  2. Calculate μ = E(X).
  3. Calculate σ2 = σ2(X).


2. Given that X has a binomial distribution with n = 10 and p = 0.30, find the following:

  1. the mean, μ 

  2. the variance, σ2. 

  3. P(X = 2) 

  1. Given that X has a Poisson distribution for which the average rate of occurrences is 0.04 per day and the length of the interval is 12 days, find the following:
    1. the mean of X 

    2. the variance of X 

  2. Assume that Y has an exponential distribution with λ = 4 per meter. Find . . .
    1. E(Y) 

    2. σ2(Y) 

  3. Suppose customers contact a health agency’s on-line help desk randomly and independently at an average rate of 6 per hour. Find . . .
  1. the average time between the beginning of one contact and the beginning of the next contact. 

  2. the average number of contacts in a 12-minute period. 

  3. the probability that there will be exactly two contacts between 4:00 and 4:12. 

  4. the probability that the length of time from now until the next contact will be more than 15 minutes. 

6. Find each of the following normal probabilities. Z has a standard normal distribution.

  1. P(Z < 1.86) 

  2. P(-0.73 < Z < 1.19) 

7.The time it takes an experienced installer to install a device in a customer’s home has a normal distribution with a mean of 52 minutes and a variance of 100 minutes2. The management wants to know the probability that an installation job will take more than one hour. Calculate this probability.


































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