STA301

STA301 3rd Assignment Solution
Q No. 1 (a): In how many ways can 4 boys and 5 girls sit in arow if every boy and girl has to sit side by side?

In order to fulfill the given condition, the seating arrangement must be asfollows.GIRL BOY GIRL BOY GIRL BOY GIRL BOY GIRL

5 girls can seat in 5 × 4 × 3 × 2 × 1 = 120 ways

4 boys can seat in 4 × 3 × 2 × 1 = 24 ways

Total number of ways in which 5 girls and 4 boys can sit fulfilling thegiven condition = 120 × 24 = 2880

Q No. 1 (b): Briefly explain the terms mutually exclusiveevents, exhaustive events and sample space.

Mutually Exclusive Events: Those events that cannot occur at the sametime.

Example: When we toss the coin, we get either Heads or Tails but not both.Exhaustive Events: Events are said to be collectively exhaustive, when the union of mutually exclusive events is the entire sample space.Example: When we toss a coin, then Heads and Tails are collectively known as Exhaustive Events.Sample Space: Sample Space is a set which consists of all possible outcomes resulting from a random experimentExample: Sample Space in case of a fair die is S = {1,2,3,4,5,6}Q No. 1 (c): A fair coin is tossed. Make a sample space and findthe probability of the followings:I. One head appearsII. One tail appearsIII. No head appearsThe sample space for a toss is S = {Heads, Tails}One head appears = . = 0.5One tail appears = . = 0.5No head appears = . = 0.5

Q No. 2 (a): In a simple linear regression yˆ = a + bx , interpret thecoefficients “a” and “b”.a is called the y-intercept, and b indicates the rate of change in y withrespect to x and is formally known as the slope of the line.

Q No. 2 (b): A computer while computing the correlationcoefficient between two variables x and y from 25 pairs ofobservations, obtained the following results:n = 25 , Σx = 125 , Σx2 = 650 , Σy = 100 , Σy2 = 460 , Σxy = 508It was, however discovered at the time of re-checking that ithad mistakenly copied down two pairs of observations asbelow:x y11 109 7While the correct values werex y14 812 9Now find out the correct value of correlation coefficientbetween x and y.Correct Σx = 125 – 11 – 9 + 14 + 12 = 131Correct Σy = 100 – 10 – 7 + 8 + 9 = 100Correct Σx2 = 650 – 112 – 92 + 142 + 122 = 788Correct Σy2 = 460 – 102 – 72 + 82 + 92 = 456Correct Σxy = 508 – (11 × 10) – (9 × 7) + (14 × 8) + (12 × 9) = 555= 0.41