If f(x) is a density with support on the entire line, is g(x)=f(x^2) a density? The same question but support of f is positive numbers. The distribution of f(x) is uniform.
If f(x) is a density with support on the entire line, is g(x)=f(x^2) a density? The...
X is a random variable with density function f(x) = x² /3 for -1 < x < 2,0 else. U is uniform(0,1). Find a function g such that g(U) has the same distribution as X.
Find the constant a such that the function is continuous on the entire real line. f(x) = [ 5x2, x 21 ax - 5, x < 1 a =
Let f(x) = z² and g(x) = (1 - 5)² + 10. There is one line with positive slope that is tangent to both of the parabolas y = f(x) and y = g(x) simultaneously. ye9bx)/ y=f/ Find the equation of the line. y= On a separate piece of paper, sketch the graph of the parabola y = 2? + 6. On the same graph, plot the point(0, – 3). Note that there are two tangent lines of y =...
1.For x ≥ 0, let f(x) = 2xe−x^2 Show that f is a density function. 2. Find the cumulative distribution for the density in the preceding exercise. 3. Find the pth quantile of this distribution.
1. Suppose that X is continuous random variable with PDF f(x) and CDF F(x). (a) Prove that if f(x) > 0 only on a single (possible infinite) interval of the real numbers then F(x) is a strictly increasing function of x over that interval. [Hint: Try proof by contradiction]. (b) Under the conditions described in part (a), find and identify the distribution of Y = F(x). 2. Suppose now that X ~ Uniform(0, 1). For each of the distributions listed...
Charge is distributed along the entire x-axis with uniform density λ. How much work does the electric field of this charge distribution do on an electron that moves along the y-axis from y = a to y = b? (Use the following as necessary: a, b, ε0, λ, and q for the charge on an electron.)
2. A line of charge with uniform density of 38.0 nC/m lies along the line y 12.0 cm between the points x 5.0 cm and 40.0 cm. Calculate the electric field (both the magnitude and direction) at the origin due to this charge distribution. (2436 N/C, 137.9°)
1. Consider the following two probability density functions: f(3) = 2053 } for a <I<02 and g() = where ci and ca are finite real numbers. 265. for <y<02, (a) Show that f(r)dx = 9(r)dt = 1. (b) Find the cumulative distribution functions F(x) and Gu). (d) Show that if X-f(x), then 1-X g(x). (e) Show that if X h(x) = 21, for 0 <<1, then Y = c +(2-c)X ~f. (h) Show that if Uſ and U2 are two...
Let X be a random variable with the probability density function f(x)= x^3/4 for an interval 0<x<2 (a) What is the support of X? (b) Letting S be the support of X, pick two numbers a, b e S and compute Pa<x<b). Draw a graph that shows an area under the curve y = f() that is equal to this probability. (c) What is Fx (2)? Draw a good graph of y=Fx (I). (d) What is EX? (e) What is...
Let g(x) = f(G), whore Ny) is continous and f(x) 20 for all x. Support that tim ndo and him g) = 0o. Determine wheller to following integrais CONVERGE DIVERGE. Explain. glx) dx be g) di g de 12 >