Let (X) be the uniform distribution for the random variable X in Example 11. Express the following probabilities as integrals. a. The probability that the

Let ƒ(X) be the uniform distribution for the random variable X in Example 11. Express the following probabilities as integrals.

a. The probability that the arrow points either between South and West or between North and West.

b. The probability that the arrow makes an angle of at least 2 radians.

EXAMPLE 11 An anchored arrow is spun around the origin, and the random variable X is the radian angle the arrow makes with the positive x-axis, measured within the inter- val [0, 27). Assuming there is equal probability for the arrow pointing in any direction, find the probability density function and the probability that the arrow ends up pointing between North and East. We model the probability density function with the uniform distribution f(x) = 1/2, 0 x < 27, and f(x) = 0 elsewhere. The probability that the arrow ends up pointing between North and East is given by /2 = 7) - 1.5 12 1/10 dx = 1 - 0 P(0 x =/ )