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3 Continuous RV

3 Continuous RV. cdf. 3-1: X is the number of heads in three tosses of a coin. Find P[1<X 2 ], P[0.5X<2.5 ], P[1X<2]. 3-2: Draw the cdf of a Zipf RV X with 3 elements . That is, for k =1,2,3. cdf vs. pdf. 3-3: Find the cdf of an RV X. Its pdf is given by:

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3 Continuous RV

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  1. 3 Continuous RV

  2. cdf • 3-1: X is the number of heads in three tosses of a coin. Find P[1<X2], P[0.5X<2.5], P[1X<2]. • 3-2: Draw the cdf of a Zipf RV X with 3 elements. That is, for k=1,2,3

  3. cdf vs. pdf • 3-3: Find the cdf of an RV X. Its pdf is given by: • 3-4: Find the cdf and pdf of the transmission time X of messages in a network. Its probability is given by an exponential distribution:

  4. expectation • 3-5: Find E[X-Y], where an RV X has cdf of , and RV Y has the pdf of • Note that X and Y are non-negative RVs

  5. Exponential RV • 3-6: Find the probability that a man who has already waited for a bus for 2 min will wait longer than total 4 min? A bus comes every 2 min on average. Inter-bus arrival times follow an exponential distribution.

  6. Normal RV • Look up Table 4.2 • 3-7: X is a normal RV with N(80,102). Find P[X>90] and P[70<X<90] • 3-8: X is a normal RV with N(80,502). Find P[X>90] and P[70<X<90]

  7. Normal RV • Look up Table 4.3 • 3-9: Scores of students are modeled by a normal RV with N(80,102). Find which score is top 10% and top 1%.

  8. Chebyshev Inequality • 3-10: if X has mean m and variance 2, Suppose X is a Gaussian RV. What is the probability that P[ |X-m|  2 ]? Use Chebyshevinequality .

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