For 10 observations on price and supply
the following data were obtained (in appropriate units):
Obtain the line of regression of Y on X and estimate the supply when price is 16 units.
To obtain the regression line of \( Y \) on \( X \), we use the equation of a simple linear regression: \[ Y = a + bX \] where: - \( _____ ____ _________ ____ __________ _________ _______ _____ ____ ____ ________ ____.
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If Find the moment generating function of x − c where c is constant.
Let Find (i) the correlation coefficient between x and y, and (ii) E( y / x) .
The probability that a student passes a Physics test is
and the probability that the student passes both a Physics test and an English test is The probability that the
student passes at least one test is What is the probability that the student passes the English test?
Let p be the probability that a coin will fall head in a single toss in order to test against
The coin is tossed 3 times and
is rejected if more than 2 heads are obtained. Find the probability of type I and type II errors. Also obtain the power of the test.
The joint probability distribution of x and y is given below:
| 0 | 1 | 2 | ||
| 0 | ||||
| 1 | ||||
| 2 | __ | |||
| 3 | __ | |||
Find (i) )
(ii) )
(iii) )
(iv) )
Which of the following statements are True or False? Give reasons for your answer.
i) If 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 then
assume only non-positive values and hence
iv) If two unbiased dice are rolled, then the probability of their same score being 6 is
v) If the random variable x follows a normal distribution with known mean µ and unknown variance then
is a statistic but ) (x −µ is not.
Find the maximum likelihood estimator for the parameter λ of the Poisson distribution on the basis of a sample of size n . Also, find its variance.