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A distribution that is said to follow mainly two properties is regarded as a discrete probability distribution. Firstly, the probabilities must be positive, and secondly, they should be 1 or below 1.

The probabilities are positive, and the summation of the probabilities of speeds is shown below:

$$\begin{gathered} \mathbf{\text{Summation=0.05+0.25+0.25+0.50}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\text{=1}} \end{gathered}$$

Therefore, as the total probability of the speeds in Section 1 is 1, the properties are satisfied.

The probabilities for speeds in Section 2 are positive, and the summation of the probabilities of speeds is shown below:

$$\begin{gathered} \mathbf{\text{Summation=0.10+0.25+0.35+0.30}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\text{=1}} \end{gathered}$$

Therefore, as the total probability of the respective speeds in Section 2 is 1, the properties are completely satisfied.

The probabilities are positive, and the summation of the probabilities of speeds is shown below:

$$\begin{gathered} \mathbf{Summation}\mathbf{=0.15+0.20+0.30+0.35} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\text{=1}} \end{gathered}$$

Therefore, as the total probability of the respective speeds in Section 3 is 1, the properties are completely satisfied.

Any city or area has certain speed limits for vehicles purring along the roads. If the vehicles at any cost cannot exceed their speed above a certain level, they will be penalised.

The probability for a vehicle to travel above 30 mph is shown below:

$$\begin{gathered} \mathbf{\text{Probability=1}}\mathbf{鈭�}\mathbf{\text{Probability}}\mathbf{(}\mathbf{\text{Speed}}\mathbf{鈮�}\mathbf{\text{30}}\mathbf{)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\text{=1}}\mathbf{鈭�}\mathbf{\text{0.05}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\text{=0.95}} \end{gathered}$$

Therefore, the probability for a vehicle to travel above 30 mph is 0.95.

The probability for a vehicle in Section 2 to travel above 30 mph is shown below:

$$\begin{gathered} \mathbf{\text{Probability=1}}\mathbf{鈭�}\mathbf{\text{Probability}}\mathbf{(}\mathbf{\text{Speed}}\mathbf{鈮�}\mathbf{\text{30}}\mathbf{)} \\ \mathbf{\text{=1}}\mathbf{鈭�}\mathbf{\text{0.10}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\text{=0.90}} \end{gathered}$$

Therefore, the probability for a vehicle in Section 2 to travel above 30 mph is 0.90.

The probability for a vehicle in Section 3 to travel above 30 mph is shown below:

$$\begin{gathered} \mathbf{\text{Probability=1}}\mathbf{鈭�}\mathbf{\text{Probability}}\mathbf{(}\mathbf{\text{Speed}}\mathbf{鈮�}\mathbf{\text{30}}\mathbf{)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\text{=1}}\mathbf{鈭�}\mathbf{\text{0.15}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\text{=0.85}} \end{gathered}$$

Therefore, the probability for a vehicle in Section 3 to travel above 30 mph is 0.85.