x is a binomial random variable. (Give your answers correct to three decimal places.)
(a) Calculate the probability of x for: n = 1, x = 0, p = 0.15
P(x) = Changed: Your submitted answer was incorrect. 0.15 x 0 = 0 .
(b) Calculate the probability of x for: n = 3, x = 3, p = 0.15
P(x) = Incorrect: Your answer is incorrect. . 0.15 x 3 = 0.45
(c) Calculate the probability of x for: n = 5, x = 0, p = 0.8
P(x) = Correct: Your answer is correct. . 0.8 x 0 = 0
(d) Calculate the probability of x for: n = 1, x = 1, p = 0.4
P(x) = Correct: Your answer is correct. . 0.4 x 1 =0.40
(e) Calculate the probability of x for: n = 3, x = 1, p = 0.45
P(x) = Incorrect: Your answer is incorrect. . 0.45 x 1 =0.45
(f) Calculate the probability of x for: n = 6, x = 6, p = 0.25
P(x) = Incorrect: Your answer is incorrect. . 0.25 x 6 = 1.50
This is what I got when I redone them.
#2 I get a different answer on this one and when I tried yours it was wrong, I got .0675 and when I worked (e). out I get a 0.6075 but that does not look right. (f) 2.25. I had got 2 answers right when I first done it and I did them all the same way and not sure how I am missing them still.
I don't know to which question 0.0675 referred.
Note that:
nCr = n!/[(n-r)!(r!)]
For (e), we have
P(n=3,x=1,p=0.45)
=3C1*0.45^1*(1-0.45)^(3-1)
=3*0.45*0.55^2
=0.408375
(f) probabilities never exceed 1!
P(n=6,x=6,p=0.25)
=6C6*0.25^6*(1-0.25)^(6-6)
=1*0.25^6
=0.000244
Sorry , I worked them out and they are all wrong. I missed b, e, and f.
To calculate the probability of a binomial random variable, you can use the binomial probability formula:
P(x) = (nCx) * p^x * (1 - p)^(n - x)
Where:
- n is the number of trials
- x is the number of successes
- p is the probability of success in a single trial
- (nCx) is the binomial coefficient, which represents the number of ways to choose x successes from n trials and is calculated as n! / (x! * (n - x)!)
Now, let's calculate the probabilities for the given values:
(a) n = 1, x = 0, p = 0.15
P(x) = (1C0) * 0.15^0 * (1 - 0.15)^(1 - 0) = 1 * 1 * 0.85 = 0.85
(b) n = 3, x = 3, p = 0.15
P(x) = (3C3) * 0.15^3 * (1 - 0.15)^(3 - 3) = 1 * 0.003375 * 1 = 0.003375
(c) n = 5, x = 0, p = 0.8
P(x) = (5C0) * 0.8^0 * (1 - 0.8)^(5 - 0) = 1 * 1 * 0.00032 = 0.00032
(d) n = 1, x = 1, p = 0.4
P(x) = (1C1) * 0.4^1 * (1 - 0.4)^(1 - 1) = 1 * 0.4 * 1 = 0.4
(e) n = 3, x = 1, p = 0.45
P(x) = (3C1) * 0.45^1 * (1 - 0.45)^(3 - 1) = 3 * 0.45 * 0.2975 = 0.4005
(f) n = 6, x = 6, p = 0.25
P(x) = (6C6) * 0.25^6 * (1 - 0.25)^(6 - 6) = 1 * 0.000244141 * 1 = 0.000244141
Now, comparing these results to the ones you provided, it seems that the calculations for (c), (d), and (e) are correct, but the calculations for (a), (b), and (f) are incorrect.
Note: The calculations assume that multiplication and exponentiation have higher precedence than other mathematical operations. Make sure to use parentheses if your calculator or software follows a different order of operations.
For a binomial distribution, the outcomes are either 1 (success) or zero (failure).
The probability of success (outcome =1)of EACH step (out of n steps) is p and remains unchanged over the duration of the experiment.
The probability of failure (outcome =0) of EACH step (out of n steps) is q=1-p and remains unchanged over the duration of the experiment.
The probability of r successes in an n-step experiment is given by:
Bin(n,p,x)
=nCx p^x q^(n-x)
where nCx = n!/((n-x)!x!)
and x=number of successes
(a)
n=1, p=0.15, q=0.85
r=0 (0 success)
P(1,0,0.15)
=1C0 0.15^0 0.85^1
=1*1*0.85
=0.85
(b)
n=3, x=3, p=0.15
P(3,3,0.15)
=3C3*0.15^3(0.85)^0
=1*0.15^3*1
=0.03375
The rest of the exercises are similar.
You can attempt them and return for an answer check.