The first three moments of a distribution about the value 2 are 1, 16 and – 40 respectively. Examine the Skewness of the distribution.
To examine the skewness of the distribution, we can use the formula for skewness:
Skewness = (3rd moment) / (standard deviation)^3
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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?
Draw the cumulative frequency curves for the following distribution:
| Marks | No. of Students |
| 0 – 10 | 4 |
| 10 – 20 | 8 |
| 20 – 30 | 11 |
| 30 – 40 | 15 |
| 40 – 50 | 12 |
| 50 – 60 | 6 |
| 60 – 70 | 3 |
An unbiased die is rolled twice. Let denote the event: odd face roll on the first die,
denote the event that total score is Odd. Check the independence of
and .
X , X and X3 is a random sample of size 3 from a population with mean µ and variance
. and
are the estimators to estimate µ, and are given by ;
and
i) Are T1 and T2 unbiased? Give reason.
ii) Find the value of λ such that T3 is unbiased.
iii) Which is the best estimator? State giving reasons.
A single observation was taken from a population with p.d.f.
Obtain confidence interval for θ.
Show that variance can be expressed in terms of the mutual differences of the observations i.e.
a) Find the mean and standard deviation for the following data:
| Class interval | Frequency |
| 0 – 10 | 5 |
| 10 – 20 | 10 |
| 20 – 30 | 14 |
| 30 – 40 | 15 |
| 40 – 50 | 6 |
b) State Chebychev’s inequality. Hence obtain the lower bound for if the E(x) and
of x are 4 and 20 respectively.