Suppose a random variable has a continuous uniform distribution between 0 and 10, such that its probability density function is: f(x) = 1/10. a. What is the cumulative density function for x? b. What is the mean (expected value) of x? c. What is the variance of x? d. According to Chebychef's rule, what is the smallest probability a random x will within 2 standard deviations of its mean? i.e. P(x-μ<2*o) e. What is the exact probability that a random x will fall within 2 standard deviations of its mean for this uniform distribution?

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**Uniform Distribution Problem**

Suppose a random variable has a continuous uniform distribution between 0 and 10, such that its probability density function is: \( f(x) = 1/10 \).

**Questions:**

a. What is the cumulative density function for \( x \)?

b. What is the mean (expected value) of \( x \)?

c. What is the variance of \( x \)?

d. According to Chebychev's rule, what is the smallest probability a random \( x \) will be within 2 standard deviations of its mean?
   - i.e. \( P(|x - \mu| < 2 \ast \sigma) \)

e. What is the exact probability that a random \( x \) will fall within 2 standard deviations of its mean for this uniform distribution?
Transcribed Image Text:**Uniform Distribution Problem** Suppose a random variable has a continuous uniform distribution between 0 and 10, such that its probability density function is: \( f(x) = 1/10 \). **Questions:** a. What is the cumulative density function for \( x \)? b. What is the mean (expected value) of \( x \)? c. What is the variance of \( x \)? d. According to Chebychev's rule, what is the smallest probability a random \( x \) will be within 2 standard deviations of its mean? - i.e. \( P(|x - \mu| < 2 \ast \sigma) \) e. What is the exact probability that a random \( x \) will fall within 2 standard deviations of its mean for this uniform distribution?
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d. According to Chebychev’s rule, what is the smallest probability a random x will within 2 standard deviations of its mean?  
i.e. \( P(|x - \mu| < 2 \ast \sigma) \)

e. What is the exact probability that a random x will fall within 2 standard deviations of its mean for this uniform distribution?
Transcribed Image Text:d. According to Chebychev’s rule, what is the smallest probability a random x will within 2 standard deviations of its mean? i.e. \( P(|x - \mu| < 2 \ast \sigma) \) e. What is the exact probability that a random x will fall within 2 standard deviations of its mean for this uniform distribution?
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