Apply Chebyshevs Inequality to lower bound P(O< X < 4) when E(X) 2 and E(X2)-5
6. If E(x) 16 and E(X?) -292, use Chebyshev's inequality to determine a) A lower bound for P(8< X < 24). (b) An upper bound for P(X 162 18)
Modify X and apply Markov's inequality to upper bound P(X > 3) when X > 2 and E[X] = 2.5.
Exercise 2 Consider a random variable X with E]5 and VarX 16 (a) Calculate P(lz-5 < 6) if X follows a normal distribution. (b) Use Chebyshev's inequality to provide a lower bound for P(-5). (No longer assume X is normal.)
Solve the inequality log2 (x2 – 3x + 4) <1. Give the answer as an interval.
Let X ~ Geomeric(p). Using Chebyshev's inequality find an upper bound for P(|X – E[X]] >b).
Solve the inequality f(x) <0, where f(x) = - x2(x + 4), by using the graph of the The solution set for f(x) <0 is. (Type your answer in interval notation.) function. Ay 4- 2- х 500 -8 -6 -4 -2 2 4. 6 -8- -104 -12-
4. The solution of the inequality x2 – 4 < 0 is (a) –2 < x or x > 2 (b) –2 < x < 2 (C) x>-2 (d) x < 2 (e) None of the above 5. The domain of the function f(x) = V2is (a) (-2,2) (b) (-0, -2) U (2,00) (c) (-0, -2] U (2,0) (d) (-20, -2] U (2,00) (e) None of the above 6. The range of the function f(x) = 2 sin(x) is (a)...
Solve the follwing rational inequality: 2 – 3 < 0 x + 1
Solve the inequality. 2x + 3 -1< 5
Define X1 = Z1, X2 = 22, ..., Xn = Zn and X = 36 L3fXi. Consider the following probability A=P('x=11<3). (d) Please provide the distribution of X and find the exact probability A (accurate to the third decimal place). (e) Please provide a lower bound for A by the Chebyshev's inequality.