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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.
Determine order and degree(if defined) of differential equation yn + 2y' + siny = 0
Let f : R → R be defined as f(x) = x4. Choose the correct answer.
(A) f is one-one onto
(B) f is many-one onto
(C) f is one-one but not onto
(D) f is neither one-one nor onto.
y = x2 + 2x + C : y' - 2x - 2 = 0
Let A and B be sets. Show that f : A × B → B × A such that f(a, b) = (b, a) is bijective function.
Determine order and degree(if defined) of differential equation ym + 2yn + y' =0