A binomial probability experiment is conducted with the given parameters. Use technology to find the probability of X successes in the n independent trials of the experiment.

n=9, p=0.25, x<4

P(x<4)=

A binomial probability experiment is conducted with the given parameters. compute the probability of X successes in the n independent trials of the experiment.

n=10, p=0.6, x=5

P(5)=

MATALB MATALAB

Getting 4-of-a-kind

Consider the following experiment:

oYou draw 5 cards from a deck of 52 cards. This is considered a single experiment. If you get 4-of-a-kind the experiment is considered a "success".

oYou repeat the experiment N=100,000 times, keeping track of the"successes".

oAfter the N experiments are completed count the total successes, andcalculate the probability of getting4-of-a-kin

Women athletes at the University of Colorado – Boulder have a long-term graduation rate of 62% (Source: The Chronicle of Higher Education). Over the past several years, a simple random sample of 42 women athletes at the school showed that 22 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the University of Colorado – Boulder is now less than 62%? Use a 5% significance level and the Traditional method.

check the requirements

Establish H0 and H1.

Is this a 2-tailed test, left-tailed, or right-tailed?

Calculate the value of the test statistic. Round to three figures after the decimal point. Use correct sign.

Determine the critical value. Use correct sign.

Is there sufficient evidence to reject the claim that the population proportion of women athletes who graduate from UC equals to 0.62?

Group of answer choices

Stet by step in R and attach R file and R codes too - Thanks

Use one of the real-world example data sets from R (not previously used in the R practice assignment) or a dataset you have found, and at least two of the tests and R functions covered in the practice assignment to conduct a hypothesis test then report your findings and give proper conclusion(s).

Use the following supporting materials for R syntax, data sets and tools, along with other resources found in this module or that you find on your own.

• Using T-Tests in R from the Department of Statistics at UC Berkley

• Test of equal or given proportions from R Documentation

• F-Test: Compare Two Variances in R from STHDA (Statistical tools for high-throughput data analysis)

Please answer step by step with R files attached and R codes

Show that if V is finite-dimensional and W is infinite-dimensional, then V and W are NOT isomorphic.

Let U be a subspace of V . Prove that dim U ⊥ = dim V −dim U.

I have a question in that if v is s any nonzero vector, and v is positioned with its initial point at the origin, then the terminal points of all scalar multiples of v will occur at all the points on a straight line through the origin. But if we want to find two vectors, let's say m and n, that are parallel to each other, we need to determine whether they are multiples of each other.

So my question here is: what's the difference between scalar multiples and multiples? In another word, vectors within the same line are parallel to each other because this would be a special form of parallel?

Questionnnnnnn

a. Let V and W be vector spaces and T : V → W a linear transformation. If {T(v1), . . . T(vn)} is linearly independent in W, show that {v1, . . . vn} is linearly independent in V .

b. Define similar matrices

c Let A1, A2 and A3 be n × n matrices. Show that if A1 is similar to A2 and A2 is similar to A3, then A1 is similar to A3.

d. Show that similar matrices have the same characteristic polynomial and eigenvalues.

e. Determine whether the following mappings are linear transformations.

T : V → R defined by T(x) = hx, vi, where v is a fixed nonzero vector in the real inner product space V .

The linear transformation is such that for any v in R², T(v) = Av.

a) Use this relation to find the image of the vectors v₁ = [-3,2]^T and v₂ = [2,3]^T. For the following transformations take k = 0.5 first then k = 3,

T₁(x,y) = (kx,y)

T₂(x,y) = (x,ky)

T₃(x,y) = (x+ky,y)

T₄(x,y) = (x,kx+y)

For T₅ take theta = (pi/4) and then theta = (pi/2)

T₅(x,y) = (cos(theta)x - sin(theta)y, sin(theta)x + cos(theta)y)

b) Plot v₁ and v₂ and their images under the transformations. Write a short description saying what the transformations is doing to the vectors.

Let V be a vector space and let U and W be subspaces of V . Show that the sum U + W = {u + w : u ∈ U and w ∈ W} is a subspace of V .