Question 1 3+6+6=15 Marks
Q.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?
Ans: Formula is given by
Q.1 (b): Briefly explain the terms mutually exclusive events, exhaustive events and sample space.
Ans:
Mutually exclusive events: Two events A and B of a single experiment are said to be mutually exclusive or disjoint if and only if they cannot both occur at the same time i.e. they have no points in common.
Exhaustive Events: Events are said to be collectively exhaustive, when the union of mutually exclusive events is equal to the entire sample space S.
Sample Space: A set consisting of all possible outcomes that can result from a random experiment (real or conceptual), can be defined as the sample space for the experiment and is denoted by the letter S.
Each possible outcome is a member of the sample space, and is called a sample point in that space.
Q.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 appear
Ans: The Sample Space is
(I) P(One head appears)=1/2
(II)P(One tail appears)=1/2
(II)P(No head appears)=1/2
Question 2 5+10 Marks
(a): In a simple linear regression , interpret the coefficients “a” and “b”.]
Ans: Y = a + bX
Where
• Y represents the dependent variable
• X represents the independent variable
• a represents the Y-intercept
(i.e. the value of Y when X is equal to zero)
• b represents the slope of the line
(i.e. the value of the tan q, where q represents the angle between the line and the horizontal axis)
(b): A computer while computing the correlation coefficient between two variables x and y from 25 pairs of observations, obtained the following results:
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.
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