Question

Step 1

**a.**

**Explain the reason behind representing x as discrete random variable:**

*Discrete random variable*:

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

The data represents the values of number of hurricanes developed corresponding to the sequence number of tropical storms within a season.

Consider the variable *x *represents the sequence number of tropical storms within a season.

The variable sequence number of tropical storms within a season takes the countable or finite values. The sequence numbers of tropical storms within a season are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 and 22.

Hence, the variable sequence number of tropical storms within a season is said to be discrete.

Step 2

**Construct the probability distribution for the variable x.**

*Conditions of the discrete probability distribution:*

- The probabilities of all the values of the variable
*X*must lie between 0 and 1. - The sum of probabilities of all the values of
*X*must be equal to “1”.

The total number of developed hurricanes is *n *= 67.

The general formula to obtain the probability of an event is,

Probability of an event *= *(Number of favourable cases for the event)/(Total number of cases).

Here, the probabilities for the values of the variable *x *is obtained as,

Probability of *x _{i}* = (Number of hurricanes developed for that particular

The probabilities for the values *x* = 1, 2, 3, 4, 5, 6 is obtained below:

Step 3

**Construct the probability distribution for the variable x.**

The probabilities for the v...

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