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inequality
Answers
Answer: When x
1
=−1 and x
2
=1, then
f(−1)−f(1)=f(
1−1(1)
−1−1
)=f(−1)⇒f(1)=0
which is satisfied when f(x)=tan
−1
(
1+x
1−x
)
when x
1
=x
2
=0, then
f(0)−f(0)=f(
1−0
0−0
)=f(0)⇒f(0)=0
when x
1
=−1 and x
2
=0, then
f(−1)−f(0)=f(
1−0
−1−0
)=f(−1)⇒f(0)=0
which is satisfied when f(x)=log(
1+x
1−x
) and f(x)=log(
1−x
1+x
)
Step-by-step explanation:
Problem 4. Solve the following problems related to Markov inequality. 1. Let X be a random variable with range X € {1,2,...,100} Assume that all values are equally likely, i.e., the pmf of X is 1 Px(i) i=1,2,...,100. 100 Calculate Pr(x > 90). Now, obtain an upper bound on this probability using Markov inequality. 2. Let Y be a random variable with range Y = {1,2,...,500). Assume that all values are equally likely, i.e., the pmf of Y is 1 Py(i)= i=1,2,...,500. 500 Calculate Pr(Y > 400). Now, obtain an upper bound on this probability using Markov inequality.