### 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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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)
A binomial experiment for the random variable X was performed with 10 trials. The probability of success was found to 0.44. Determine the following probabilities: [Round to four decimal places.] a.) P(X = 4)= b.) P(X 6) =
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
The finish of a hole depends on the edge of the bit used, only 1% of the holes with a new drill have an irregular cut, 3% have an irregular cut with average bits and 5% present irregular cut with worn bits. If 25% of the holes are made with new bits, 60% have average edges and 15% are worn out. [use 3 decimal places] a) If a piece is taken at random, what is the probability of having holes irregular? b) If a piece with irregular holes is taken, what is the probability that would have been made with an average drill bit?
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The time between arrivals of customers at an automatic teller machine (ATM) is an exponential random variable with a mean of five minutes. a) What is the probability that the time until the third customer arrives in more than 10 minutes? b) what is the value for σ2 for the third customer? c) what is the value for σσ for the third customer ?

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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