For each of the following exercies, determine if the random variable has a discr

Question

For each of the following exercies, determine if the random variable has a discrete uniform, binomial, or none of these distributions.

Problem 1: 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) a) 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 b) Defects occur randomly over the surface off a semiconductor chip. However, only 80% of defects can be found by testing. A sample of 40 chips is tested. Let the random variable is the number of chips in which the test finds a defect. c) The random variable is the moisture content of a lot of raw material d) 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

(a) Here the number of parts is Random Variable X which is a discrete distribution. values of X are integers where X = 0,1,2,3,.... it is not a binomial distribution because it is not success out of n because n is not there.

(b) Here n = 40 and p = 0.80 so this is binomial distribution. Where expected success = 40* 0.80 = 32 .

(c) Here the random variable is a continuous variable because moisture content can take any value so it is continuous.

(d) Here X is the first digit of the serial number so it is discrete distribution X can take values from 0 to 9 .

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