Chapters: Expected value & Variance of a continuous random variable **Q1.** A box is to be constructed so that its height is five inches and its base is $ Y $ inches by $ Y $ inches, where $ Y $ is a random variable described by the probability density function (pdf), $ f(y) = 6y(1-y) $, $ 0 < y < 1 $. Find the expected value of the volume of the box.---**Q2.** Let $ X $ be a random variable with the probability density function $ f(x) = 3(1-x)^2 $ when $ 0 \leq x \leq 1 $ and $ f(x) = 0 $ otherwise.**a.** Verify that $ f $ is a valid pdf.**b.** Find the mean and variance of $ X $.**c.** Find $ P(X \leq 1/2) $.**d.** Find $ P(X \leq 1/2|X \geq 1/4) $.

I solved exactly first question because of bartleby policy if you want more please uplode separately..

Q1. A box is to be constructed so that its height is five inches and its base is Y inches by Y inches, where Y is a random variable described by the pdf, f(y) = 6y(1 – y), 0 < y < 1. Find the expected value of the volume of the box.

Q1. A box is to be constructed so that its height is five inches and its base is Y inches by Y inches, where Y is a random variable described by the pdf, f(y) = 6y(1 – y), 0 < y < 1. Find the expected value of the volume of the box.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: Explain the difference between the one-way fixed effects model and the one-way random effects model.

Q: Example 8-15. Determine the binomial distribution for which the mean is 4 and variance 3 and find…

Q: If X is normal random variable with mean 3 and variance 5, then find the probability P(2 < X <6).

Q: What are Gamma Random Variables?

Q: What is the expectation of X where X is a single roll of a fair 6-sided dice (S {1,2, 3, 4, 5, 6})?…

Q: EU A: master Test the significance of the main effects and interaction effect by creating the…

A: Two way ANOVA:The ANOVA (Analysis of variance) test compares the means of different samples and the…

Q: The random variables X and Y have joint pdf (x(1+3y²) fxy (x, y) = 0 < x < 2, 0< y < 1 4 0,…

A: Solution: The joint pdf of (X,Y) is given by fXY(x,y)=x(1+3y2)4 0<x<2, 0<y< 10…

Q: How can we use discrete random variables in statistics?

A: Solution: Discrete random variable: A variable is said to be discrete if it takes the positive…

Q: Sample Variance State the null and alternative hypotheses. Ho : oO H : o> Calculate the value of the…

A: It is given that For current method, sample size n1 = 41, sample variance s12 = 21 For new method,…

Q: Pediatric asthma survey, n = 50. Suppose that asthma affects 1 in 20 children in a population. You…

Q: Fast answer please

A: The question is asking whether the variance of the product of two independent random variables X and…

Q: How can you determine if a random variable is discrete or continuous?

A: Introduction A variable is a characteristic that is being measured.

Q: If the variance of the discrete random variable X = 36

A: Variance is 36

Q: It is the measure of association between two random variables obtained as the expected value of the…

Q: If X is a random variable having a normal distribu-tion, what are the probabilities of getting a…

Q: Next question hearts? An experiment consists of dealing 4 cards from a standard 52-card deck. What…

A: no.of heart cards=13total no.of cards=52

Q: 1 example solution of mean and variance using Negative Binomial Distribution.

Q: If we have heterogeneity of variance - other than we violated an assumption of the test , what else…

A: Given information: One boxplot of protein and another boxplot of log (Protein) are given, comparing…

Q: Define the Mean and Variance of Sums of Random Variables?

A: The mean of a random variable X is a weighted average of the possible values that the random…

Q: in a binomial distribution, if n= 4 and p = 1/3 then the value of variance is?

A: Given: n = 4 probability of success (p) = 1/3

Q: The combined probability distribution of two random variables is referred to as its marginal…

Q: The number of customers buying a cooked breakfast at a high-street cafe on a weekday morning is a…

Q: To conduct a hypothesis test comparing two population variances, both pop must be normally…

A: Assumptions for two sample variance test: Two populations should be normally distributed. Two…

Q: What is the expected value of an exponential randomvariable?

A: Exponential random variable. For a positive constant k>0, the exponential density function (with…

Q: In analysis of variance, what is the purpose of the mean square between and the mean square within?…

A: Analysis of variance (ANOVA) is the method used to test the means of three or more groups…

Q: 1. ) Please answer the following questions in only 1-2 sentences for each part: (a) What is the…

A: 1.(a).Disjoint events and independent events are different. Events are considered disjoint if they…

Q: Consider the following two-way table Disease 19 15 No disease Risk factor No risk factor Calculate…

A: Probability could be defined as the number of favorable outcomes divided by the number of possible…

Q: Discuss in which instances can Correlation and Covariance be equal to each other for the two random…

A: We know that correlation is defined as the ratio of covariance between two variables to the square…

Q: An insurance company sells insurance policies. Each insurance policy leads to claims with expected…

A: Here, x is random variable which denoting price of each insurance policy. y is random variable…

Q: Yorkies Company has fixed costs of 25000 per month, variable costs are $20 per item produced, and…

A: fixed costs = 25000 per month variable costs = $20 per item produced selling price per unit is fixed…

Q: (1 point) If X is a binomial random variable, compute the mean, the standard deviation, and the…

Q: You know that the sample mean, X. is the minimum variance unbiased estimator of . with a variance of…

Q: You run a house flipping business where you buy thousands of houses across the country, hire…

A: . For any given house is a 50%/50% chance of gaining 60% or losing 40%. This means expected return…

Q: Random samples of a Gaussian distribution will fall within two standard deviations of the mean with…

A: Concept: 68% of the data is within 1 standard deviation (σ) of the mean (μ), 95% of the data is…

Q: Example 42. Show that for the Binomial distribution with parameters n and p: (a) Variance is less…

Q: Briefly describe one-way analysis of variance using at least the following questions: • In what…

A: As the name suggests, Analysis of Variance (ANOVA) is used to analyze the variance of the observed…

Question

Chapters: Expected value & Variance of a continuous random variable

**Q1.** A box is to be constructed so that its height is five inches and its base is $ Y $ inches by $ Y $ inches, where $ Y $ is a random variable described by the probability density function (pdf), $ f(y) = 6y(1-y) $, $ 0 < y < 1 $. Find the expected value of the volume of the box.

---

**Q2.** Let $ X $ be a random variable with the probability density function $ f(x) = 3(1-x)^2 $ when $ 0 \leq x \leq 1 $ and $ f(x) = 0 $ otherwise.

**a.** Verify that $ f $ is a valid pdf.

**b.** Find the mean and variance of $ X $.

**c.** Find $ P(X \leq 1/2) $.

**d.** Find $ P(X \leq 1/2|X \geq 1/4) $.

Video Video

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

The expected value of a discrete random variable always corresponds to an actual outcome that may occur.
A nutritionist claims that children 13 to 15 years old are consuming less than the recommended iron intake of 20.5 mg. To test the nutritionist's claim of iron deficiency, a random sample of children 13 to 15 years old will be obtained. Assume that the data for iron intake follows the normal distribution with a standard deviation of 4.75 mg. Find the size of the sample that you should take if you want to estimate the true mean iron intake to within 1 mg with 99% confidence. 62 149 O 150 O 61
Multivariate analysis is a statistical principle that involves observation and analysis of more than one statistical outcome variable at a time. O True False
1. How do you determine the values of a random variable? 2. How do you know whether a random variable is continuous or discrete? What is the difference between the two types of random variables?
Textbook: Statistics for the Behavioral SciencesGregory J. Privitera Please show your work-Concept and Application Problems (Pg.133) If Sample 1 has a variance of 4 and Sample 2 has variance of 32, can we tell which sample had a larger range? If so, which sample had a greater range?
I asked this question before, and got an answer, but I have a question about the response that was given. The original question was: For an initial investment of 100, an investment yields returns of X1 and X2, where X1 and X2 are independent normal random variables with mean 60 and variance 25. What is the probability that the rate of return of this investment is greater than 10%? In the answer that was given it says that the gain of the investment is X1+X2. My question is why can we just group those together as one amount? I was given a formula in my class that says the return on the investment would be the solution to the equation: -100+ X1/(1+r) + X2/(1+r)2=0. If this formula is used, a different solution would result for this problem.
Please answer this ASAP TOPIC: Variance and Covariance of Random Variable
You own a company called Company X, which has monthly sales that are independent normal random variables with mean 100 and variance 10. Your rival company, called Company Y, has monthly sales that are independent normal random variables with mean 110 and variance 20. (a) Find the probability that your company, Company X, makes more than $307 this quarter (a quarter is 3 months). (b) What is the probability that your company makes more money than your rival company this month?
A description of the distribution of the values of a random variable and their associated probabilities is called a probability distribution random variance random variable expected value
Discuss Exponential Random Variables.