Gomez.Assignment4B - Jordan Gomez Lesson 15 Cumulative Distribution Function 1 The CDF of our random variable X is 2 t F t)=(1525 t 15 t 23 t 3 4 for 0

# Gomez.Assignment4B - Jordan Gomez Lesson 15 Cumulative...

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Jordan Gomez Lesson 15 Cumulative Distribution Function 1. The CDF of our random variable X is F ( t ) = t 2 4 ( 15 25 t + 15 t 2 3 t 3 ) for 0 ≤t ≤ 2. a. Calculate the probability of { 1 2 ≤ X ≤ 1 } . P { 1 2 ≤ X ≤ 1 } = F ( 1 ) F ( 1 2 ) ¿ 1 4 ( 15 25 + 15 3 ) 1 16 ( 15 25 2 + 15 4 3 8 ) ¿ 1 2 47 128 ¿ 0.1328 b. Find the density of X . f ( x ) = d dt F ( t ) ¿ 15 t 2 75 t 2 4 + 15 t 3 15 t 4 4 ¿ 15 t 4 ( 2 5 t + 4 t 2 t 3 ) ¿ 15 t 4 ( 2 t ) ( t 1 ) 2 2.For a random variable Wwhere P{W=0}=0.1and P{W=1}=0.2and the density of W for values between 0 and 1 is f(w)=1.4w ,draw a graph of the CDF. Is this a valid probability distribution? 1.
for 1 ≤r≤ 0 for 0 < r ≤ 1 elsewhere F(w) Lesson 16 Normal Distribution 3.A SAT score is designed to have a normal distribution with mean 400 and standard deviation 200. If we take 5 independent SAT scores, what is the probability that the mean of them is greater than 500?

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• Winter '09
• LANDRIGAN
• Normal Distribution, Probability distribution, Probability theory, probability density function, CDF