Which of the following statements are True or False? Give reasons for

Question

Which of the following statements are True or False? Give reasons for your answer.
i) If $y=ax-b,$ then the correlation coefficient between x and y does not exist and if it exists it is equal to zero.
ii) For a normal distribution mean, median and standard deviation are all equal.
iii) If $x\geq y$ then $y-x$ assume only non-positive values and hence $E(x)\leq E(y).$
iv) If two unbiased dice are rolled, then the probability of their same score being 6 is $\frac{1}{6}.$

v) If the random variable x follows a normal distribution with known mean µ and unknown variance $\sigma ^2$ then $\frac{x-\mu }{\sigma }$ is a statistic but ) (x −µ is not.

12 Mar 2024

Answer :

Word Count : 250

i) False – If y=ax−by = ax - b, the correlation coefficient between xx and yy exists and is equal to ±1\pm 1, depending on the sign of aa. The correlation coefficient does not become zero unless a=0a = 0, in __________ __________ _________ __________ ________ _________.
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