Mathematics

Determine whether each of the following is true or false. If true, prove the statement. If false, find a counterexample.

Mathematics, Other Math / By

Determine whether each of the following is true or false. If true, prove the statement. If false, find a counterexample. a) For all integers a, b,and c, if a | b and a | c then a | (3b − 5c). b) For all integers a ≥ 4 and b, if a | 3b then …

Determine whether each of the following is true or false. If true, prove the statement. If false, find a counterexample. Read More »

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?

Mathematics, Probability and Statistics / By

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.

Mathematics, Advanced Math / By

EXPERT ANSWER