Question

Here students are asked to consider a continuous random variable X with probability densit function if 1 < x < 2 f(x) = = { a cos x+b sin x x2 0 otherwise. It is given that E(X) = 1.317. (a) Find the values of the constants a and b. You may use Maple to assist with your calculations. Answer: a = Number b= Number Give your answers for a and b to at least four decimal places, for example, 0.1234 Explain briefly how you solved this problem, making reference to any formulae you used involvin probability density functions, expected values and so on. 這 Q 1= 2= 三三三三皇 Ω Equation Editor A A T B T U = x x Styles Font Size Submit Assignment Quit & Save Back Question Menu Next

Answer 1

To find the values of the constants a and b in a continuous random variable with a given probability density function, we can use the expected value formula. In this case, we can set up an integral and solve it to find the values of a and b. The final answers should be provided to at least four decimal places.

Step-by-step explanation:

To find the values of the constants a and b, we can use the fact that the expected value of X is given as E(X) = 1.317. The expected value of a continuous random variable X with probability density function (pdf) f(x) is calculated as: E(X) = ∫xf(x)dx. In this case, we have a piecewise-defined pdf: f(x) = { a cos(x) + b sin(x) if 1 < x < 2, 0 otherwise. Thus, using the given information, we have: 1.317 = ∫12(a cos(x) + b sin(x)) dx

To solve this integral, we can use Maple or any other integration tool. Once we have the anti-derivative of (a cos(x) + b sin(x)), we can substitute the limits of integration to find the value of a and b. The final answers should be provided to at least four decimal places.