For each of the following exercises, determine If the random variable has a disc

Question

For each of the following exercises, determine If the random variable has a discrete uniform, binomial or none of these distributions. For the variables with discrete uniform or binomial, report the value(s) of parameter(s). There is a 2% chance to select a machined part that do not conform to customer requirements the random variable is the number of parts in a sample of 5, machined parts that do not conform to customer requirements. There is a 2% chance to select a machined part that do not conform to customer requirements Parts are selected successively, without replacement, until a nonconforming part is obtained. The random variable is the number of parts selected. The random variable is the moisture content of a lot of raw material. The first digit of a part's serial number is equally likely to be any one of the digits 0 through 9 One part is selected from a large batch and X is the first digit of the serial number

Explanation / Answer

First we define discrete uniform distribution and binomial distribution.

Discrete Uniform Distribution :

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n.

Binomial Distribution :

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p

The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N.

If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution, not a binomial one.

a) The random variable X is the number of parts in a sample of machined parts that do not conform to customer requirements.

Here X has Binomial distribution with n = 5 and p = 2%.

b) Here the random variable has neither Binomial nor discrete uniform distribution.

Random variable follows Hypergeometric distribution.

c) The random variable is the moisture content of a lot of raw material, measured to the nearest percentage point.

And we know that percentage is in integer so the variable is continuous.

It is neither discrete uniform nor binomial.

d) Here the random variable is the first digit of the serial numbers.

Each time probability is 1/11 bacause there are 11 numbers (0-9)

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