Mathematics

8. In Bangladesh, 40% of male smokers smoke cigars. In a randomly selected sample of 20 male smokers, what is the probability that a. (2 mark) exactly 4 of the men smoke cigars? b. (2 marks) at most 3 of the men smoke cigars? c. (2 marks) at least 2 of the men smoke cigars? d. (3 marks) What are the expected value, variance, and standard Deviation of the above random variable?

EXPERT ANSWER Binomial distribution is used when the number of observations n is fixed, each observation is independent and also Each observation has two outcomes either success (p) or failure (q) and the probability of success p is the same for each outcome. Binomial distribution is used when the number of observations n is fixed, …

8. In Bangladesh, 40% of male smokers smoke cigars. In a randomly selected sample of 20 male smokers, what is the probability that a. (2 mark) exactly 4 of the men smoke cigars? b. (2 marks) at most 3 of the men smoke cigars? c. (2 marks) at least 2 of the men smoke cigars? d. (3 marks) What are the expected value, variance, and standard Deviation of the above random variable? Read More »

A more general and also complicated love between Romeo and Juliet is the IVP⎩⎨⎧​R˙=f(t,R,J),J˙=g(t,R,J),R(0)=R0​,J(0)=J0​,​wherefandgare two real functions dependent ont,R, andJ. Similarly, find conditions onfandgso that the IVP SYS. (14) has a solution. For example, a solution exists for IVP SyS. (14) wheref(R,J)=R(1−J)andg(R,J)=J(R−1)(this is also known as the Lotka-Volterra equations in Biology to model the interaction of two species). Give five specific examples of such IVPs without finding the exact solutions.

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