PROBABILITY AND STATISTICS

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Presentation transcript:

PROBABILITY AND STATISTICS WEEK 6 Onur Doğan

Continuous Random Variables and Probability Distributions Onur Doğan

Example Suppose that the probability density function of X is; Determine P(X < 2) , P(2 ≤ X < 4) , and P(X≥4) Onur Doğan

Cumulative Distribution Functions Onur Doğan

Example Determine the cumulative distribution function of X. (for previous question) Onur Doğan

Mean and Variance of a Continuous Random Variable Onur Doğan

Example Determine the mean, variance, and standard deviation of X. (for previous question) Onur Doğan

Continuous Uniform Distribution Onur Doğan

The Exponential Distributions Onur Doğan

Example The number of customers who come to a donut store follows a Poisson process with a mean of 5 customers every 10 minutes. Determine the probability density function of the time (X; unit: min.) until the next customer arrives. Find the probability that there are no customers for at least 2 minutes by using the corresponding exponential and Poisson distributions. How much time passes, until the next customer arrival Find the variance? Onur Doğan