Let A, B, and C be independent random variables, uniformly distributed over [0,9], [0,2], and [0,3] respectively. What is the probability that both roots of the equation Ax^2+Bx+C=0 are real?
f(a,b,c)= | (1/((a2-a1)*(b2-b1)*(c2-c1))= | 1/54 |
probability=∫c1b2^2/4a2 ∫ a1a2 ∫√4acb2 f(a,b,c) db da dc +∫b2^2/4a2c2 ∫ b1b2 ∫0b^2/4c f(a,b,c) da db dc | ||||||||
=f(a,b,c)*(b2*(a2-a1)*(b22/4a2-c1)-(8/9)*((b22/4a2-c1)*(a2-a1))3/2)+f(x)*(b23/12)*(ln(c2)-ln(b22/4a2)) | ||||||||
=0.0206+0.0407 | ||||||||
=0.0613 |
Let A, B, and C be independent random variables, uniformly distributed over [0,9], [0,2], and [0,3]...
Let ?, ?, and ? be independent random variables, uniformly distributed over [0,5], [0,1], and [0,2] respectively. What is the probability that both roots of the equation ??^2+??+?=0 are real?
(1 point) Let A, B, and C be independent random variables, uniformly distributed over [0,4], [O,7], and [0, 6] respectively. What is the probability that both roots of the equation Ax2 Bx+ C = 0 are real? (1 point) Let A, B, and C be independent random variables, uniformly distributed over [0,4], [O,7], and [0, 6] respectively. What is the probability that both roots of the equation Ax2 Bx+ C = 0 are real?
Let A, B, and C be independent random variables, uniformly distributed over [0,6], [0,7], and [0,11] respectively. What is the probability that both roots of the equation Ax2+Bx+C=0 are real?
1 point) If a is uniformly distributed over [−27,23], what is the probability that the roots of the equation x2+ax+a+80=0 are both real? (1 point) If a is uniformly distributed over [-27, 23), what is the probability that the roots of the equation r+ ax + a + 80 = 0 are both real?
Рroblem 5. Let X1. X2,.. be independent random variables that are uniformly distributed over [-1.1. Show that the sequence Yı , V2.... converges in probability to some limit, and ident ify the limit, for each of the following cases: (а) Ү, Хn/п. n
Let Y_(1) and Y_(2) be independent and uniformly distributed random variables over the interval (0,1). Find P(2 Y_(1)<Y_(2)).
Let X and Y be independent random variables uniformly distributed on the interval [1,2]. What is the moment generating function of X + 2Y? Let X and Y be independent random variables uniformly distributed on the interval [1,2]. What is the moment generating function of X + 2Y?
Consider two independent random variables X1 and X2. (continuous) uniformly distributed over (0,1). Let Y by the maximum of the two random variables with cumulative distribution function Fy(y). Find Fy (y) where y=0.9. Show all work solution = 0.81
4.3. Let X and Y be independent random variables uniformly distributed over the interval [θ-, θ + ] for some fixed θ. Show that W X-Y has a distribution that is independent of θ with density function for lwl > 1.
1 & 2 pls Let U be a uniformly distributed random variable on [0, 1]. What is the probability that the equation x2 + 4-U、x + 1 = 0 has two distinct real roots x1 and x2? 1. 2. The probability that an electron is at a distance r from the center of the nucleus is: with R being a scale constant. a) Find the value of the constant C. b) Find the mean radius f. c) Find the standard...