Question: A point (a,b) is chosen from the square R = {0 a 1,0 b 1}. Suppose that the probability distribution on

A point (a,b) is chosen from the square R = {0 ≤ a ≤ 1,0 ≤ b ≤ 1}. Suppose that the probability distribution on R is uniform; that is, the probability that a point (a,b) comes from a region in R, equals the area of this region.

(a) Find the probabilities that a ≥ b and 2a ≥ b.

(b) Consider the quadratic equation x² + 2ax +b = 0 with the coefficients (a,b). Find the probability that the equation has real solutions; has only one real solution.

Step by Step Solution

★★★★★

3.43 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

12 a The problem is illustrated in FigM1 a Pa b equal... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Probability And Stochastic Modeling Questions!

1. Elaine is a chemist. (C) 2. Nancy is not a sales clerk. (S) 3. Neither Wordsworth nor Shelley was Irish. (I) 4. Rachel is either a journalist or a newscaster. (J, N) 5. Intel designs a faster chip...

Suppose that a point (X, Y) is to be chosen from the square S in the xy-plane containing all points (x, y) such that 0 x 1 and 0 y 1. Suppose that the probability that the chosen point will be...

You own 800 shares of XYZ Travel Tours which you purchased for $52.40 a share. Puts on the company's stock sell for $1.85 for a strike price of $55. What will be the cost to obtain this strike price?

Suppose that a point X1 is chosen from the uniform distribution on the interval [0, 1], and that after the value X1 = X1 is observed, a point X2 is chosen from a uniform distribution on the interval...

Reliability of a robotic device. The reliability of a piece of equipment is frequently defined to be the probability, p, that the equipment performs its intended function successfully for a given...

plz solve it asap ty I U [1 point] (g) Calculate the PDF for Y. [3 points] Include your working for each part. Please select file(s) Select file(s) Q4 Joint Probability 5 Points Two continuous random...

2) Is Pink the best mix of Red and White? There's no rule that says a portfolio has to be an equal mix of two investments. (a) Find the mean and variance of a portfolio that has 60% invested in White...

Assume the random variable x is normally distributed with mean u = 50 and standard deviation 6 = 7. Find the indicated probability. P(x > 38) P(x > 38) = D (Round to four decimal places as needed.)...

1 1 point A random variable x is normally distributed with a mean of 117 and a standard deviation of 14. What is the probability of selecting any random variable from the distribution with a value...

VERY QUICK AND EASY. DONT NEED TO SHOW WORK Hello please help ASAP! Please TYPE the answer back to me, you can send the screenshots back and write on them. *** On this assignment, I am allowed 2...

You are designing SecureBox, an authenticated online file storage system. For simplicity, there is only a single folder. Users must be able to add, edit, delete, and retrieve files, and to list the...

Please mention and explain the ratio on liquidity, profitability, and solvency (choose only 3 ratios each).

You run a healthcare clinic called Sunny Shores and have collected the following visit and cost data provided in the table below. Fill in the table by calculating the average costs and marginal costs

Visit the Federal Trade Commission ( www.ftc.gov ) and Better Business Bureau ( www.bbb.org ) sites. What ethical and legal issues involving marketing to children appear?

Let $\left(X_{t}, \mathscr{F}_{t}ight)_{t \geqslant 0}$ be a martingale and denote by $\mathscr{F}_{t}^{*}$ be the completion of $\mathscr{F}_{t}$ (completion means to add all subsets of...

Let $\left(B_{t}ight)_{t \geqslant 0}$ be a $\mathrm{BM}^{d}$ and assume that $X$ is a $d$-dimensional random variable which is independent of $\mathscr{F}_{\infty}^{B}$. a) Show that...

Let $F: \mathbb{R} ightarrow[0,1]$ be a distribution function. a) Show that there exists a probability space $(\Omega, \mathscr{A}, \mathbb{P})$ and a random variable $X$ such that...

c++ Compare efficiency of linear probing, quadratic probing, and separate chaining.

Una empresa que no implementa controles de calidad efectivos, en qu paso del proceso de gestin falla?: A. Planificacin B. Direccin C. Control D. Toma de decisiones

Suppose Marys stock has a standard deviation of 45%, while Harry stock has a standard deviation of 35%. If the correlation between these stocks is 0.1, what is the standard deviation of a portfolio...