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StatisticsQ&A Library6.2 Dental Insurance You plan to purchase dental insuranceTRY for your three remaining years in school. The insurancemakes a one-time payment of $1,000 in case of a majordental repair (such as an implant) or $100 in case of aminor repair (such as a cavity). If you don't need dentalrepair over the next 3 years, the insurance expires and youreceive no payout. You estimate the chances of requiringa major repair over the next 3 years as 5%, a minor repairas 60% and no repair as 35%.a. Why is X = payout of dental insurance a randomvariable?b. Is X discrete or continuous? What are its possiblevalues?c. Give the probability distribution of X.tho prob.Question

Asked Oct 11, 2019

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Step 1

a.

*Random variable:*

A random variable, usually denoted as *X*, is a variable whose possible values are numerical outcomes of a random phenomenon. In other words, it is a variable that is subject to random variations so that it can take on multiple different values, each with an associated probability.

There are two types of random variables, discrete and continuous.

Here, the random variable *X* is defined as the pay out of dental insurance.

The variable, pay out of dental insurance is random and it depends on whether you need minor, major or no dental repair over the next three years.

Step 2

**b .**

*Discrete random variable***:**

If the variable *X* takes finite or countable values, then the variable *X* is said to be discrete.

Here, the random variable *X* takes values, $1,000, $100 and $0.

Thus, the random variable takes only a finite number of distinct values.

That is, *X *is a discrete random variable.

Step 3

**c.**

*Probability distribution:*

The probability distribution of a discrete random variable is the list of probabilities associated with each of its possible values.

The following requirements should be satisfied for the distribution to follow discrete probability distribution.

- The given random variable (
*X*) must take up finite or countable...

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