For a Poisson distributed random variable X, P(X = 4) = P(X = 5).What is the mean and variance of the distribution?
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For the following data
| x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| f | 1 | 9 | 26 | 59 | 72 | 52 | 29 | 7 | 1 |
If a random variable U has the t-distribution with n degrees of freedom, show that Z = U2 has the F-distribution with 1 and n degrees of freedom.
Let X1 ,X2 ,...,Xn be a random sample from a normal population, N(.Obtain a (1-
) level confidence interval for
when
is unknown.
The height of 100 students of a study centre of IGNOU is approximately normally distributed with mean () 65 inches and standard deviation (
) 2.5 inches. Find the number of students whose height is
i) less than 65 inches,
ii) between 60 inches and 70 inches.
hich of the following statements are true or false? Give reasons for your answer.
i) If P(A) = 0.5, P(A È B) = 0.7 and A and B are independent events, then P(B) = .
ii) There exists a random variable X for which
.
iii) If X has the distribution N(10, 9) and if Y = 5X + 3, then Y has distribution N(53,81).
iv) The abscissa of the point of intersection of two gives of less-than type and more- than type gives the mean of the data.
v) In a problem of testing of a simple hypothesis against a simple alternative, if the probability of type 1 error is known to be 0.06, then the power of the test will be 0.94.
If X is a random variable with E(X) = 3and E(X2) = 16, find a lower bound for the probability P[-2 < X < 8].
For the following frequency table obtain the relative frequencies and the cumulative frequencies of the ‘more than’ type.
| Life (in hours)
499.5 – 649.5 | Frequency
5 |
| 649.5 – 799.5 | 20 |
| 799.5 – 949.5 | 40 |
| 949.5 – 1099.5 | 81 |
| 1099.5 – 1249.5 | 57 |
| 1249.5 – 1399.5 | 34 |
| 1399.5 – 1549.5 | 13 |
| Total | 250 |