Let X be the number of students who attend counseling at a certain time of day....

Let X be the number of students who attend counseling at a certain time of day. Suppose that the probability mass function is as follows p (0) = .15, p (1) = .20, p (2) = .30, p (3) = .25, and p (4) = .10. Determine:

a) Is this a valid probability mass function? Why?

b) Obtain the cumulative probability function

c) What is the probability that at least two students come to counseling

d) What is the probability that, from one to three students, inclusive, they will come to counseling e) Obtain the average and standard deviation of the probability function. Interpret your results.

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Let X equal the number of female children in a three-child family. Among students who were...

Let X equal the number of female children in a three-child family. Among students who were taking statistics, 52 came from families with three children. For these families x = 0, 1, 2, and 3 for 5, 17, 24, and 6 families, respectively. (a) Conduct a Chi-square goodness-of-fit test to test the null hypothesis that the distribution of X is B(3, 0.5) at 0.05 significance level. (b) Conduct a Chi-square goodness-of-fit test to test the null hypothesis that the distribution...

Let x be the number of years after 2007 and y represent the number of students...

Let x be the number of years after 2007 and y represent the number of students enrolled at WWCC. Answer the following given the data that enrollment was 2055 in the year 2007, 2244 in 2008, 2512 in 2009, and 2715 in 2010. (a) Find the least-squares line for the data using Excel and submit your file in Canvas. (b) Using partial derivatives, verify the formula you obtained in Excel. (c) Find the least-squares error E.

Let x be the number of courses for which a randomly selected student at a certain...

Let x be the number of courses for which a randomly selected student at a certain university is registered. The probability distribution of x appears in the table shown below: x 1 2 3 4 5 6 7 p(x) .05 .03 .09 .26 .37 .16 .04 (a) What is P(x = 4)? P(x = 4) = (b) What is P(x 4)? P(x 4) = (c) What is the probability that the selected student is taking at most five courses? P(at...

For the population of Cal Poly students, let X = number of hours slept in the...

For the population of Cal Poly students, let X = number of hours slept in the last 24 hours and Y = number of exams today. Consider the following (admittedly simplistic) joint probability distribution for Xand Y. x 5 6 7 8 0 .01 .09 .16 .18 y 1 .11 .06 .04 .02 2 .28 .02 .02 .01 For your convenience, I have calculated the following: ?(?)=6.24,?(?2)=40.34,?(?)=0.89,?(?2)=1.55E(X)=6.24,E(X2)=40.34,E(Y)=0.89,E(Y2)=1.55. A. Determine the marginal distribution of X. B. Calculate E(XY). C. Calculate the correlation between X...

Let X be the number of heads and let Y be the number of tails in...

Let X be the number of heads and let Y be the number of tails in 6 flips of a fair coin. Show that E(X · Y ) 6= E(X)E(Y ).

A university planner is interested in determining the percentage of spring semester students who will attend...

A university planner is interested in determining the percentage of spring semester students who will attend summer school. She takes a pilot sample of 160 spring semester students discovering that 56 will return to summer school. Construct a 90% confidence interval estimate for the percentage of spring semester students who will return to summer school. Construct a 95% confidence interval estimate for the percentage of spring semester students who will return to summer school.

a) A university planner wants to determine the proportion of spring semester students who will attend...

a) A university planner wants to determine the proportion of spring semester students who will attend summer school. She surveys 40 current students discovering that 15 will return for summer school.At 90% confidence, compute the margin of error for the estimation of this proportion. b) A university planner wants to determine the proportion of spring semester students who will attend summer school. She surveys 36 current students discovering that 16 will return for summer school.At 90% confidence, compute the lower...

Once an individual has been infected with a certain disease, let X represent the time (days)...

Once an individual has been infected with a certain disease, let X represent the time (days) that elapses before the individual becomes infectious. An article proposes a Weibull distribution with α = 2.6, β = 1.1, and γ = 0.5. [Hint: The two-parameter Weibull distribution can be generalized by introducing a third parameter γ, called a threshold or location parameter: replace x in the equation below, f(x; α, β) = α βα xα − 1e−(x/β)α x ≥ 0 0 x...

Once an individual has been infected with a certain disease, let X represent the time (days)...

Once an individual has been infected with a certain disease, let X represent the time (days) that elapses before the individual becomes infectious. The article “The Probability of Containment for Multitype Branching Process Models for Emerging Epidemics” (J. of Applied Probability, 2011: 173-188) proposes a Weibull distribution with alpha = 2.2, beta = 1.1, and gamma = 0.5 a. Calculate P(1 < X < 2). b. Calculate P(X > 1.5). c. What is the 90th percentile of the distribution? d....

A random sample of 1000 eligible voters is drawn. Let X = the number who actually...

A random sample of 1000 eligible voters is drawn. Let X = the number who actually voted in the last election. It is known that 60% of all eligible voters did vote. a) Find the approximate probability that 620 people in the sample voted, and b) Find the approximate probability that more than 620 people in the sample voted.

Subjects