6:
Since coin is fair so probability of getting a head in a single trial is 0.5. Here X will have binomial distribution with parameters n=10 and p=0.5.
That is
7:
Sample size is 40. Using CLT will have approximately normal distribution with mean
and variance
So,
conducts an experiment in which they tip a coin 10 times and count of heads. Let the random represent varlable X represent the number of heads. Write the distribution of x In a class of 40 studen...
A fair coin is tossed four times and let x represent the number of heads which comes out a. Find the probability distribution corresponding to the random variable x b. Find the expectation and variance of the probability distribution of the random variable x
Let random variable x represent the number of heads when a fair coin is tossed two times. a) construct a table describing probability distribution b) determine the mean and standard deviation of x (round to 2 decimal places)
An experiment consists of tossing a coin 6 times. Let X be the random variable that is the number of heads in the outcome. Find the mean and variance of X.
Conduct the random experiment of flipping a coin five times. Let X be the number of heads. (a) Compute P(X > 3). (Round your answer to four decimal places.) (b) Compute E(X).
let x be the random variable that represent the lenght of time it takes a student to complete maths 23 exam. it was found that x has an approximately normal distribution with mean 1.5 hours and standard deviation =025 hours. (a) what is the probability that it takes at least 1.4 hours for a randomly selected student to complete the exam? (b) suppose 25 students are selected at random,what is the probability that the mean time x of completing the...
Let the random variable x represent the number of girls in a family with three children. Assume the probability of a child being a girl is 0.31. The table on the right describes the probability of having x number of girls. Determine whether the table describes a probability distribution. If it does, find the mean and standard deviation. Is it unusual for a family of three children to consist of three girls? 0 1 2 3 P(x) 0.329 0.443 0.199...
In-class worksheet - Binomial distribution Date: 1. Which of the following situations describe a Binomial random variable? (a) Let X be the number of tosses of a fair coin until you obtain a head. (b) The probability of a girl having black hair is 0.6. There are 6 girls altogether. Let X be the number of girls out of the 6 who have black hair. (c) Among 6 girls, there are two with black hair. You pick 4 girls at...
1. Suppose that random variables X and Y are independent and have the following properties: E(X) = 5, Var(X) = 2, E(Y ) = −2, E(Y 2) = 7. Compute the following. (a) E(X + Y ). (b) Var(2X − 3Y ) (c) E(X2 + 5) (d) The standard deviation of Y . 2. Consider the following data set: �x = {90, 88, 93, 87, 85, 95, 92} (a) Compute x¯. (b) Compute the standard deviation of this set. 3....
Let X be normally distributed with mean 100 cm and standard deviation 5 cm. (a) On the diagram below, shade the region representing P(X > 105). (2) (b) Given that P(X < d) = P(X > 105), find the value of d. (2) (c) Given that P(X > 105) = 0.16 (correct to two significant figures), find P(d < X < 105). (2) (Total 6 marks) 2. A test has five questions. To pass the test, at least three of...