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22:06 10月20日周日

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HW4 HW4 开始播入页面审阅衧图效室 R. WPS AI Times 小四

A^{*}

$A^...

Oct 20, 2024

Solution by Steps

step 1

To develop the empirical discrete probability distribution for

x

, we first need to calculate the total number of graduates surveyed, which is

N = 506 + 390 + 310 + 218 + 576 = 2000

step 2

Next, we calculate the probability for each value of

x

(the number of years with the current employer) using the formula:

P(x) = \frac{\text{Number of graduates with } x \text{ years}}{N}

. The probabilities are: - For

x = 1

P(1) = \frac{506}{2000} = 0.253

- For

x = 2

P(2) = \frac{390}{2000} = 0.195

- For

x = 3

P(3) = \frac{310}{2000} = 0.155

- For

x = 4

P(4) = \frac{218}{2000} = 0.109

- For

x = 5

P(5) = \frac{576}{2000} = 0.288

step 3

To verify that this is a valid discrete probability distribution, we check that all probabilities are between 0 and 1 and that they sum to 1:

P(1) + P(2) + P(3) + P(4) + P(5) = 0.253 + 0.195 + 0.155 + 0.109 + 0.288 = 1.000

step 4

To find the probability that a respondent has been at their current place of employment for more than 3 years, we calculate: P(x > 3) = P(4) + P(5) = 0.109 + 0.288 = 0.397

Answer

The empirical discrete probability distribution is valid, and the probability that a respondent has been employed for more than 3 years is 0.397.

Key Concept

Empirical discrete probability distribution and its validation.

Explanation

The solution involves calculating probabilities based on observed frequencies and ensuring they meet the criteria for a valid distribution. The final probability indicates the likelihood of longer employment durations.