2. Define the random variable X as the proportion of voters in a certain county that approve of a new proposal, | cx (1 – x) 0

2. Define the random variable X as the proportion of voters in a certain county that approve of a<br>new proposal,<br>| cx (1 – x) 0 < x < 1<br>f (x)<br>otherwise<br>p<br>er<br>

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where c E R is a constant. a. Find the value of c that makes this function a valid probability density function. b. Find the cumulative distribution function, F(x), of X. c. What is the probability that more than 75% (0.75) of voters approve of the new proposal ? d. What is the probability that exactly 75% of voters approve of the new proposal ?

where c E R is a constant.<br>a. Find the value of c that makes this function a valid probability density function.<br>b. Find the cumulative distribution function, F(x), of X.<br>c. What is the probability that more than 75% (0.75) of voters approve of the new proposal ?<br>d. What is the probability that exactly 75% of voters approve of the new proposal ?<br>

Extracted text: where c E R is a constant. a. Find the value of c that makes this function a valid probability density function. b. Find the cumulative distribution function, F(x), of X. c. What is the probability that more than 75% (0.75) of voters approve of the new proposal ? d. What is the probability that exactly 75% of voters approve of the new proposal ?

Jun 07, 2022

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2. Define the random variable X as the proportion of voters in a certain county that approve of a new proposal, | cx (1 – x) 0

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