STA301 Solution

Q No. 1 (a): In how many ways can 4 boys and 5 girls sit in a

row if every boy and girl has to sit side by side?

In order to fulfill the given condition, the seating arrangement must be as

follows.

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 the

given condition = 120 × 24 = 2880

Q No. 1 (b): Briefly explain the terms mutually exclusive

events, exhaustive events and sample space.

Mutually Exclusive Events: Those events that cannot occur at the same

time.

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 experiment

Example: 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 find

the probability of the followings:

I. One head appears

II. One tail appears

III. No head appears

The sample space for a toss is S = {Heads, Tails}

One head appears = . = 0.5

One tail appears = . = 0.5

No head appears = . = 0.5

Q No. 2 (a): In a simple linear regression yˆ = a + bx , interpret the

coefficients “a” and “b”.

a is called the y-intercept, and b indicates the rate of change in y with

respect to x and is formally known as the slope of the line.

Q No. 2 (b): A computer while computing the correlation

coefficient between two variables x and y from 25 pairs of

observations, obtained the following results:

n = 25 , Σx = 125 , Σx2 = 650 , Σy = 100 , Σy2 = 460 , Σxy = 508

It was, however discovered at the time of re-checking that it

had mistakenly copied down two pairs of observations as

below:

x y

11 10

9 7

While the correct values were

x y

14 8

12 9

Now find out the correct value of correlation coefficient

between x and y.

Correct Σx = 125 – 11 – 9 + 14 + 12 = 131

Correct Σy = 100 – 10 – 7 + 8 + 9 = 100

Correct Σx2 = 650 – 112 – 92 + 142 + 122 = 788

Correct Σy2 = 460 – 102 – 72 + 82 + 92 = 456

Correct Σxy = 508 – (11 × 10) – (9 × 7) + (14 × 8) + (12 × 9) = 555

= 0.41