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

Design an experiment to knock out a certain gene of interest in the human genome. Outline the experiment, explaining the methods you would use, and also indicate how you would verify your experiment was successful at each step.

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 .

Suppose u, and v are vectors in R m, such that ∥u∥ = 1, ∥v∥ = 4, ∥u + v∥ = 5. Find the inner product 〈u, v〉.

Suppose {a1, · · · ak} are orthonormal vectors in R m. Show that {a1, · · · ak} is a linearly independent set.