State whether the following statements are true or false and also give

Question

State whether the following statements are true or false and also give the reason in support of your answer:

(a) if $X_1,X_2,X_3,\dots,X_n\text{and}Y_1,Y_2,Y_3,\dots,Y_n$ are the variate values of two variables X and and their geometric means are Grand G₂, respectively, then geometric mean of $(x_j/y_i);\quad i=1,2,\dots,n$ will be (G₁/G₂).

(b) If X and Y are two independent variables and the variables U=X+ Y and V= X-Y, then the

$r(U,V)=\frac{\sigma_x^{22}-\gamma\sigma}{\sigma_x^{22}+\gamma\sigma}$

(d) The mean and standard deviation of a set of values are 25 and 5, respectively. If a constant value 5 is added to each value, the coefficient of variation of the new set of values is equal to 10%.

(e) If $(A)=90,\quad(AB)=40,\quad N=150\text{and}(\beta)=80\text{then}(\alpha\beta)=30.$

20 Feb 2025

Answer :

Word Count : 232

(a) False.
The geometric mean of the ratio $ X/Y $ is not necessarily $ G_1/G_2 $. The geometric mean of a ratio is given by the ratio of the geometric means only if the values of $ X $ and $ Y $ are perfectly proportional, which is not always the case.

(b) False. ________ ___ _______ _____ ______ _______ ______ ________ __________ ________.
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No. of Accidents (x)	Frequencies (f)
0	46
1	?
2	?
3	25
4	10
5	5
Total	200

Age Group	No. of Workers
20 — 25	50
25 — 30	70
30 — 35	100
35 — 40	180
40 — 45	150
45 — 50	120
50 — 55	70
55 — 60	60