Suppose o, B, and y are independent Uniform(0, 1) random variables. Find the probability that ax + 3x + 7 = 0 has real roots. To facilitate the compu- tation of a numerical answer , you may use software to evaluate the integral at the end. 10 point Hints: 1. U ~ Uniform (0, 1), then - In(U) ~ Exponential(1). 2. If X ~ gamma(a, B), then cX ~ gamma(a, cB), c > 0 3. If Xi ~ gamma(ai, B), then > 1 Xi ~gamma (Xzai, B), where Xi, i = 1, 2, 3...,n are independent random variables.

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