The values of ∴a and B are (0,0), (0, 1), (0,2), (0,3), (1, 0), (1) respectively.
The first number represents the value of a, the second number represents the value of b, and the total number of basic events is 12.
When the equation x2+ax+b=0 has no solution, that is, △ = a2-4b < 0, the values of a and b are (0, 1), (0, 2), (0, 3), (1, 1), (/)
When the equation x2+ax+b=0 has a solution, that is, △=a2-4b=0, the values of a and b are (0,0) and (2 1) respectively, and the number of basic events involved is 2.
When the equation x2+ax+b=0 has two solutions, namely △ = a2-4b > 0, the values of a and b are (1, 0) and (2,0) respectively, and the number of basic events involved is 2.
The number of real roots of the equation x2+ax+b=0 is represented by a random variable ξ, so ξ = 0, 1, 2 is obtained.
So p (zeta = 0) = 812 = 23, p (zeta =1) = 212 =16, p (zeta = 2) = 2/kloc-.
The list of ∴ξdistribution is:
ξ 0 1 ? The mathematical expectation of 2p2316/6∴ξis e ξ = 0× 23+16+2×16 =12.
(2)∫a takes any number in the interval [0,2], and B takes any number in the interval [0,2].
Then all the test results form an area ω = {(a, b)|0≤a≤2, 0≤b≤2} This is a rectangular area with an area of sω = 2× 2 = 4.
Let "Equation x2+ax+b=0 has real roots" as event A,
Then the area formed by event A is M={(a, b)|0≤a≤2, 0≤b≤2, a2-4b≥0}, and its area SM = 23 can be obtained from the integral formula.
The probability p (a) = 234 = 16 can be obtained from the probability formula of geometric probability.