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Given that,

Calculate the probability sum as follows:

Sum of probabilities

$$\begin{gathered} =0.301+0.176+鈥�.+0.046 \\ =1 \end{gathered}$$

The probability range from $0$ to $1$, and the sum of the probabilities equals $1$. As a result, the probability distribution supplied is a valid probability distribution.

Given that,

The graph might be made as follows:

The graph's right side contains the majority of the data. As a result, the distribution is slanted right.

Given that,

To explain: The $X鈮�6$. Calculate the $P(X鈮�6)$ as well.

$6$or more digits are implied by $X鈮�6$. It simply signifies that there are at least six digits.

$P(X鈮�6)$may be determined using the following formula:

$$\begin{gathered} \begin{array}{c}P(X鈮�6)=P(X=6)+P(X=7)+P(X=8)+P(X=9)\end{array} \\ =0.067+0.058+0.051+0.046 \\ =0.222 \end{gathered}$$

Given that,

In terms of $X$, the event "first digit is at most $5$" may be expressed as $X鈮�5$. $P(X鈮�5)$can be computed as:

$\begin{array}{l}P(X鈮�5)=P(X=1)+P(X=2)+.........+P(X=5)\\ =0.301+0.176+........+0.079\\ =0.778\end{array}$