A man tosses a fair coin 10 times. Find the probability that he will have: (i) heads on the first five tosses and tails on the next five tosses, (ii) heads on tosses 1,3,5,7,9 and tails on 2,4,6,8,10 tosses, (iii) 5 heads and 5 tails,
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
(a) A man tosses a fair coin 10 times. Find the
(i) heads on the first five tosses and tails on the next five tosses,
(ii) heads on tosses 1,3,5,7,9 and tails on 2,4,6,8,10 tosses,
(iii) 5 heads and 5 tails,
(iv) at least 5 heads, and
(v) not more than 5 heads.
(b) Consider a binomial random variable ? with parameters ? and ?. Let
? = ?/? be a new random. Show that the
variance of ? is ??/?. If ?(?) is the ?. ?. ?. for ?, show that ??~?(?, ?).
What are the possible values that Y can take on?
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