Page 190 - Engineering Mathematics Workbook_Final

Probability & Statistics

163. A point is randomly selected with (i) What is the mean of the
uniform probability in the XY-plane distribution?
with in the rectangle with corners at
(0,0), (1,0), (1,2) and (0,2). If P is the (a) 37.2 (b) 38.1
length of the position vector of the (c) 39.2 (d) 40.2

2
point, the expected value of p is
(ii) What is the median of the
2 distribution?
(a) (b) 1
3 (a) 37 (b) 38

4 5 (c) 39 (d) 40
(c) (d)
3 3
(iii) What is the mode of the
164. A passenger arrives at a bus stop at distribution?
10 AM, knowing that bus will arrive
at some time uniformly distributed (a) 38.33 (b) 40.66
between 10 AM and 10:30 AM (c) 42.66 (d) 43.33

167. The mean of five observations is 4
(i) What is the probability that he will
have to wait longer than 10 minutes. and their variance is 5.2. If the first
three values are 1, 2 and 6, then the
(ii) If at 10.15 AM the bus has not yet remaining two values are
arrived, what is the probability that he
will have to wait atleast 10 additional (a) 2 and 9 (b) 3 and 8

minutes. (c) 4 and 7 (d) 5 and 6

Statistics 168. The two lines of regression are
−
=
2x − − 20 0, 2y x + =
y
4 0
165. For the sample 27, 35, 40, 35, 36, 36,
29, find mean, median, mode and (i) The correlation coefficient is
standard deviation.
1 1
166. Consider the following frequency (a) 2 (b) −
2
distribution
1 1
Class Frequency (c) − (d)
0-10 4 4 4
10-20 5
20-30 7
30-40 10
40-50 12
50-60 8
60-70 4

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