EXAMSHARE

Western Delta University, Oghara Delta State

department of mathematics
college of natural and applied sciences
western delta university

first semester examination 2022/2023 session

mth211 - statistics time: 1hr: 30mins

answer four (4) questions

  1. Question 1

    1. Computer the spearman rank correlation coefficient between these course MTH211 and CSC 201 for the given scores sand predict the relationship between them
      MTH21135403365576128144768
      CSC2017867975942
      (10 marks)
    2. State the axium of probability (3 marks)
    3. Prove that Q2(x) = E(x2) - E(x)2 (4.5 marks)

  2. Question 2

    1. A random variable X is defined as the sum of faces when a pair of dice is thrown find
      1. The Sample points (5 marks)
      2. Expected value of X (5 marks)
      3. Var (x) (7.5 marks)

  3. Question 3

    1. The data below rotates the weekly maintenance cost (N) to the age (in month) of ten machines of formula types in a manufacturing company
      Age (X)5101520303030505060
      Cost (Y)19242530313330303539
      1. Find the least square regression line of maintenance cost (y) on age (X)
      2. Predict the maintenance cost for the machine of this type which is 40 months old
      (17.5 marks)

  4. Question 4

    1. Suppose A and B are two events, not necessarily independent or mutually exclusive and suppose they are related. Use on diagram to show that P(AUB) = P(A) * P(B) - P(AnB) (7 marks)
    2. Three out of every batch of 30 manufactures articles pf a company are known to be defective if 5 of the articles are picked at random. What is the probability that:
      1. Exactly 2
      2. Not more than 2
      3. at most 4 are defective
      (10.5 marks)

  5. Question 5

    1. The continuous random variable X has probability density function (pdf) given by:
      F(X) =
      {1/b-a, a < x < bO, otherwise
      Find the E(X) (9.5 marks)
    2. A manufacturer produces items such that 20 percent are defective and 80 percent are non defective. If a defective items is produced, the manufacturer loses N5 while a non defective items fetches a profit of N20. Find the expected value of the profit per items (8 marks)

  6. Question 6

    1. State the properties of variance (7 marks)
    2. The discrete random variable X has a probability non function given in the table below. Find var (X)
      X = X0123
      P(X) = P(X-X)1/8 3/8 3/8 1/8
      (10.5 marks)