### Computing Binomial ProbabilitiesIf \( X \) is a binomial random variable, compute the following probabilities:a) For \( n = 4 \) and \( p = 0.5 \):\[P(X \leq 1) = 0.3125\]b) For \( n = 7 \) and \( p = 0.2 \):\[P(X > 4) = 0.08315136\]c) For \( n = 9 \) and \( p = 0.8 \):\[P(X < 5) = 0.938457216\]d) For \( n = 4 \) and \( p = 0.9 \):\[P(X \geq 2) = 0.9963\]For each calculation:- \( n \) is the number of trials.- \( p \) is the probability of success on a single trial.- \( X \) represents the number of successes in \( n \) trials. These probabilities are computed using the properties of the binomial distribution:\[P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}\]where \(\binom{n}{k}\) is the binomial coefficient.The exact values are generally found using statistical software or binomial probability tables.

X is binomial random variable with parameters number of trials (n) and probability of success (p).

Answered: If X is a binomial random variable,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Q3 a) In a binomial distribution containing of 10 independent trials, probability of 1 and 2 successes are 0.3874205 and 0.937102respectively. Find the parameter p of the distribution. b) Suppose X is a binomial random variable with parameters of n=3 and p. If P(X= 1) = 0.3, P(X= 2) = 0.2 and P(X= 0) = 3P (X = 3). Find E(X).
Q8) Find the variance of the following probability * distribution 1 4 f(x) 0.29 0.12 0.52 0.07 0.6891 O 0.8256 O 0.251 O 0.9636 O 0.9531 O
a) A player will win if he rolls two dies and gets a sum equal to 6. If he plays 12 times, what is the probability that he gets at least 2 wins? b) Suppose that the number of customers that enter a bank in an hour is a Poisson random variable, and suppose that P(X =0) = 0.02. i. What is the probability that at most one person enter the bank in one hour? ii. Determine the mean and standard deviation of X.
Suppose a random variable, x, arises from a binomial experiment with p = 0.26, n = 15. Find P(x ≤ 3): (Give answer as a decimal correct to four decimal places.)Find P(x ≥ 9): (Give answer as a decimal correct to four decimal places.)Find P(x = 7): (Give answer as a decimal correct to four decimal places.)
For a continuous random variable X, P(25 ≤ X ≤ 73) = 0.28 and P(X > 73) = 0.12. Calculate the following probabilities. (Round your answers to 2 decimal places.) a. P(X < 73) b. P(X < 25) c. P(X = 73)
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An experiment can result in one of five equally likely simple events, E₁, E₂, A: E₂, E4 2' P(A) = = 0.4 B: E₁, E3, E4, E5 P(B) = 0.8 C: E₂, E3 Refer to the following probabilities. P(A n B) = 0.2 P(AIB) = 0.25 P(BIA) P(BU C) = 1 P(BIC) 0.5 P(CIB) 0.25 Use the Addition and Multiplication Rules to find the following probabilities. (a) P(AUB) (b) P(An B) = 0.5 P(A U B) = ---Select--- + ---Select--- ✓ P(A n B) = ---Select--- (c) P(B n C) Yes P(B n C) = ---Select--- No P(C) = 0.4 . P(B) = = P(C) = = ---Select--- V = Do the results agree with those obtained by listing the simple events in each? P(A U B) = P({E₁, E₂, E3, E4, E5}) = 1 P(A n B) = P({E₁}) = 0.2 P(B n C) = P({E3}) = 0.2 .., E5. Events A, B, and C are defined as follows.
Only handwritten
What is one property of a stationary time series? Question 23 options: The datapoints demonstrate a clear seasonal pattern The mean remains constant over time It is plotted as a straight horizontal line It demonstrates an upward trend
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If X is a binomial random variable, compute the following probabilities: a) n = 4, p = 0.5 P(X ≤ 1) = 0.3125 b) n = 7, p = 0.2 P(X> 4) = 0.08315136 c) n = 9, p = 0.8 P(X<5)= 0.938457216