Page 191 - Engineering Mathematics Workbook_Final

Probability & Statistics
−
1 v = X Y what will be the
(ii) If  = , then what is  is
y x correlation coefficient between u &
4
equal to v?

1 (a) 0.433 (b) 0.333
(a) 1 (b)
2 (c) 0.233 (d) 0.133

1 171. The properties for a bivariate
(c) (d) 4
4 distribution of two random variables

X and Y are given below.
(iii) The means of x and y are
( ) 36,
( ) 24,
E X = E Y =
4
(a) x = 12, y = −
( ) 1524 ,
E X 2 = E Y 2 =
( ) 702
4
(b) x = − 12, y =
E ( XY =
) 1004
4
(c) x = − 12, y = −
The correlation coefficient between X
(d) x = 12, y = 4 and Y is

169. Correlation between two variables X 172. If byx = 0.7 and bxy = 0.2 then r =
and Y is given to be 0.6. These ___________.

variables are transformed to new
variables u = − 2X + 3 and Hypothesis Testing

v = 5Y − 2 173. To determine whether the mean
breaking strength of synthetic fibre
What will be the correlation
coefficient between u & v? produced by a certain company is 8
kg or not, a random sample of 50
(a) 0.6 fibres were tested yielding a mean
breaking strength of 7.8 kg with a
(b) -0.6
standard deviation of 0.5 kg. Test at

(c) 0.2 0.01 level of significance
(Z = 2.575 ) .
(d) Information is insufficient  /2

174. Can it be concluded that the average
170. Correlation between two variables X
1 life span of Indians is more than 70
and Y is given to be and their years if a random sample of 100
2 Indians has an average life span of
variances 36 & 16 respectively. 71.8 hours with a standard deviation
These variables are transformed to
the new variables u = X Y and
+

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