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RANDOM VARIABLE ANE DISCRETE PROBABILITY DISTRIBUTION — Statistics STD 12 Commerce — Question

Gujarat BoardEnglish MediumSTD 12 CommerceStatisticsRANDOM VARIABLE ANE DISCRETE PROBABILITY DISTRIBUTION3 Marks
Question
State properties of binomial distribution.
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Answer

Properties of binomial distribution are as follows:
- It is a probability distribution of discrete random variable.
- The parameters of this distribution are $n$ and $p$.
- The mean of the distribution is $\mathrm{np}$, which shows the average number of successes in $\mathrm{n}$ Bernoulli trials.
- In this distribution the value of its variance is always less than its mean. i.e.. $n p q-$ If for any value of $n . p=\frac{1}{2}$, it is symmetric distribution.
- If for any value of $n, p<\frac{1}{2}$, the skewness of the distribution is positive. $(8)$ If for any value of $n$, $p>\frac{1}{2}$, the skewness of the distribution is negative.

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