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Q1 Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E). Ans: It is given that P(E) = 0.6, P(F) = 0.3, and P(E ∩ F) = 0.2
In this chapter, we will learn some new aspects of probability like conditional probability etc. All the concepts which we have studied in previous classes will help us in understanding these new topics in a better way. Topics which are included in this chapter - conditional probability, multiplication theorem on probability, independent events, Bayes theorem, total probability, random variable and its probability distribution, mean and variance, Binomial distribution.
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Q1 | Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E). |
Ans: | It is given that P(E) = 0.6, P(F) = 0.3, and P(E ∩ F) = 0.2 |
In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.
(i) f : R → R defined by f(x) = 3 – 4x
(ii) f : R → R defined by f(x) = 1 + x2
Show that the Modulus Function f : R → R, given by f(x) = |x|, is neither oneone nor onto, where | x | is x, if x is positive or 0 and |x| is – x, if x is negative.
Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.
Show that the Signum Function f : R → R, given by
is neither one-one nor onto.
The total revenue in Rupees received from the sale of x units of a product is given by
R (x) = 13x2 + 26x + 15
Find the marginal revenue when x = 7.
In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.
(i) f : R → R defined by f(x) = 3 – 4x
(ii) f : R → R defined by f(x) = 1 + x2
Let f : N → N be defined by
State whether the function f is bijective. Justify your answer.
Show that the function f : R* → R* defined by f(x) = 1/x is one-one and onto,where R* is the set of all non-zero real numbers. Is the result true, if the domain R* is replaced by N with co-domain being same as R* ?
If f(x) = , show that fof(x) = x, for all x ≠ 2/3. What is the inverse of f ?