Question

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Answer 1

Answer: x 0 1 2 3

p(x) 0.011 0.170 0.279 0.539

Given that the values of x =

Television 0 1 2 3

Household 30 443 727 1401

Let television be = x

Household = frequency = distribution

Firstly, we need to find the interval of x

The interval of x = Range between two numbers

1 - 0 = 1

2 -1 = 1

3 - 2 = 1

Hence, the interval is 1

`p(x)\text{ = }\frac{frequency\text{ for x interval}}{N\text{ x w}}`

Where N = total frequency

w = interval

Total frequency = 30 + 443 + 727 + 1401

Total frequency = 2601

`\begin{gathered} \text{when x = 0} \\ p(x)\text{ = }\frac{30}{2601\text{ x 1}} \\ p(x)\text{ = }(30)/(2601) \\ p(x)\text{ = }0.011 \end{gathered}`

when x = 1

`\begin{gathered} p(x)\text{ = }\frac{443}{2601\text{ x 1}} \\ p(x)\text{ = }(443)/(2601) \\ p(x)\text{ = 0}.170 \end{gathered}`

When x = 2

`\begin{gathered} p(x)\text{ = }\frac{727}{2601\text{ x 1}} \\ p(x)\text{ = }(727)/(2601) \\ p(x)\text{ = 0.279} \end{gathered}`

when x = 3

`\begin{gathered} p(x)\text{ = }\frac{1401}{1\text{ x 2601}} \\ p(x)\text{ = }(1401)/(2601) \\ p(x)\text{ = 0.539} \end{gathered}`

Therefore,

x 0 1 2 3

p(x) 0.011 0.170 0.279 0.539