Math 331 Applied Probability & Statistics Chapter 3 Assessment write up the solu
ID: 3229511 • Letter: M
Question
Math 331 Applied Probability & Statistics Chapter 3 Assessment write up the solutions to the following questions neatly on a separate sheet of paper. Due: Wednesday, May 3 by 5pm. 1. Classify the following random variables as discrete or continuous: x: the number of automobile accidents per year in Maryland. Y: the height of a randomly selected giraffe. M: the exact time it takes to complete this exam. N: the number of students in a classroom. P: the weight of grain produced per acre. Q: the number of hits to a website in a day. 2. Let w be a random variable giving the number of heads minus the number of tails in three tosses of a coin. tosses of the a. List the elements of the sample space s for the three coin and to each sample point assign a value w of W. b. Find the probability distribution of the random variable W, assuming that the coin is biased so that a head is twice as likely to occur as a tail c. Find the cumulative distribution function, F(w), of the random variable W. d. Using F(w), find P(w 0) and P(-1swk3). 3. A continuous random variable Xthat can assume values between x 2 and xs5 has a density function given by f(x) 2(1+x)/27. Find PIXk4) and P(3sX2).Explanation / Answer
Q1)
x: This is discrete since number of accidents is fixed number which can be represented with a whole number
Y: This is continuous because height can't generally represented by a whole number. for eg a height could be 171.0 or 171.00001 or 171.001. So ther is always some sorts of approximation and we take 171 in such cases which is the most appropriate number
M: Discrete because we can represent it with exact whole number
N: Discrete because we can represent it with exact whole number
P: It is a continuous variable. Heights and weights are always continuous because of the reason mentioned for Y
Q: Discrete because we can represent it with exact whole number
(Max we can solve is 1 question or 3 subparts. I have solved complete Q1)