91影视

The first property which needs to be verified is whether the sum of all the properties is equivalent to 1, and this probability distribution verifies that as shown below:

$$\begin{gathered} \mathbf{\text{厂耻尘尘补迟颈辞苍鈥塷蹿鈥塼丑别鈥塸谤辞产补产颈濒颈迟颈别蝉=0.10+0.39+0.40+0.11}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1} \end{gathered}$$

The second property is that the probabilities must be between 0 and 1, and this distribution showcases that all the probabilities are within that range.Each of the four probabilities is greater than 0 and less than 1.

The probability distribution must contain probabilities of different values of x, which must lie between 0 and 1. The probabilities of the four responses follow those criteria in this case.

The calculation $\mathbf{\text{P}}\mathbf{\left(}\mathbf{\text{x>2}}\mathbf{\right)}$is shown below:

role="math" localid="1653639865341" $$\begin{gathered} \mathbf{\text{P}}\mathbf{\left(}\mathbf{\text{x>2}}\mathbf{\right)}\mathbf{\text{=P}}\mathbf{\left(}\mathbf{\text{x=3}}\mathbf{\right)}\mathbf{\text{+P}}\mathbf{\left(}\mathbf{\text{x=4}}\mathbf{\right)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\text{=0.40+0.11}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\text{=0.51}} \end{gathered}$$

Therefore, the$\mathbf{\text{P}}\mathbf{\left(}\mathbf{\text{x>2}}\mathbf{\right)}$ is 0.51

The formula for calculating $\mathbf{\text{E}}\mathbf{\left(}\mathbf{\text{x}}\mathbf{\right)}$is shown below:

$\mathbf{\text{E}}\mathbf{\left(}\mathbf{\text{x}}\mathbf{\right)}\mathbf{\text{=厂耻尘尘补迟颈辞苍鈥塷蹿鈥墄辫}}\mathbf{\left(}\mathbf{\text{x}}\mathbf{\right)}$

Here,$\mathbf{X}$ it represents the responses and$\mathbf{p}\mathbf{\left(}\mathbf{x}\mathbf{\right)}$ represents the associated probabilities.

The calculation $\mathbf{\text{E}}\mathbf{\left(}\mathbf{\text{x}}\mathbf{\right)}$ is shown below:

$$\begin{gathered} \mathbf{\text{E}}\mathbf{\left(}\mathbf{\text{x}}\mathbf{\right)}\mathbf{\text{=1脳0.10+2脳0.39+3脳0.40+4脳0.11}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\text{=0.10+0.78+1.20+0.44}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\text{=2.52}} \end{gathered}$$

Therefore, the $\mathbf{E}\mathbf{\left(}\mathbf{x}\mathbf{\right)}$ is 2.52, which indicates the mean of the responses by taking the associated probabilities of occurrences.