Find numbers A and B which are fixed and positive such that f(x) = Bx is a probability density function on [0; A] with a median of 3.
Find numbers A and B which are fixed and positive such that f(x) = Bx is...
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution function F,(x) f()dt of X and Var(X) (c) Let A be any Borel set of R. Define P by P(A) [,f dm 5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution...
3. Let X be a continuous random variable with probability density function ax2 + bx f(0) = -{ { for 0 < x <1 otherwise 0 where a and b are constants. If E(X) = 0.75, find a, b, and Var(X). 4. Show that an exponential random variable is memoryless. That is, if X is exponential with parameter > 0, then P(X > s+t | X > s) = P(X > t) for s,t> 0 Hint: see example 5.1 in...
Exercise 12. Show that the function p(x) = (x,Bx) + (p, x), for a fixed matrix B and a fixed vector p, is a convex function if and only if B is positive semi-definite. Exercise 12. Show that the function p(x) = (x,Bx) + (p, x), for a fixed matrix B and a fixed vector p, is a convex function if and only if B is positive semi-definite.
A continuous random variable X has probability density function f(x) = a for −2 < x < 0 bx for 0 < x ≤ 1 0 otherwise where a and b are constants. It is known that E(X) = 0. (a) Determine a and b. (b) Find Var(X) (c) Find the median of X, i.e. a number m such that P(X ≤ m) = 1/2
[4+3+3 Points] 9. For the following probability density function, f(x) -k for 0 <x < 0.5 f(x) - 3x2 for 0.5 < x < 1 f(x) -0 otherwise What is the value of k? Find the median value of x Find the probability that X<0.75 a. b.
Let x be a continuous random variable over [a,b] with probability density function f. Then the median of the x-values is m that number m for which f(x) dx = Find the median. f(x)=ke-kx e-10,00) The median is m=
The graph of a function of the form f(x)=ax^2 + bx + c for different values of a, b, and c is given. For the function, find the following. (a) Determine if the discriminant is positive, negative, or zero. (b) Determine if there are 0, 1, or 2 real solutions to f(x)=0. (c) Solve the equation f(x)=0.
A probability density function f(x) is an important concept in statistical sciences. It gives you the distribution of the random variable x. f(x) usually defined in a certain interval, and vanish in the rest. One can defined the median u and variances o2 as using the probability density function as (you'll see more about this later on in the course of statistic): u=L" xf(x)dx 2= (x – u)? dx For most cases the distribution function is normal or Gaussian. If...
Find f'(x) f(x) = x х Consider the function f(x) = 5x + x Bx a. Find f'(x) b. Find the x-values where the tangent line is horizontal Use the product rule to differentiate. Do Not Simplify y = (7x4 - x + 2)(x5 + 4)
The probability density function for a Weibull random variable with positive parameters and KS x>0 (a) Find expressions for the population mean, median, and mode. (Hint: they might not all be closed-form.) (b) Find parameter values associated with the following three cases: the population me- dian and mode of the distribution are equal; the population mean and median of the distribution are equal; the population mean and mode of the distribution are equal. The probability density function for a Weibull...