Kaushal Nair

University of Wisconsin - Madison
Tutor

Biography

I was a tutor at UW-Madison's Mathematics Learning Center and tutored courses such as pre-Calculus, Calculus, Probability Theory, Linear Algebra and Differential Equations for ten to twelve hours per week.

Education

BS Mathematics
University of Wisconsin - Madison

Educator Statistics

Numerade tutor for 4 years
435 Students Helped

Topics Covered

Differential Equations Made Simple: Expert Tips & Resources
Unlock the Power of Vectors: Discover Their Limitless Possibilities
Mastering Multiple Integrals: Techniques and Tips
Functions

Kaushal's Textbook Answer Videos

0:00
Calculus

In Exercises 23 and $24,$ copy vectors $\mathbf{u}, \mathbf{v},$ and to tail as needed to sketch the indicated vector.
$\begin{array}{ll}{\text { a. } \mathbf{u}+\mathbf{v}} & {\text { b. } \mathbf{u}+\mathbf{v}+\mathbf{w}} \\ {c.} {\mathbf{u}-\mathbf{v}} & {\text { d. } \mathbf{u}-\mathbf{w}}\end{array}$

Chapter 12: Vectors and the Geometry of Space
Section 2: Vectors
Kaushal Nair
0:00
Calculus

Copy vectors $\mathbf{u}, \mathbf{v},$ and $\mathbf{w}$ head to tail as needed to sketch the indicated vector.
a. $\mathbf{u}-\mathbf{v}$
b. $\mathbf{u}-\mathbf{v}+\mathbf{w}$
c. $2 \mathbf{u}-\mathbf{v}$
d. $\mathbf{u}+\mathbf{v}+\mathbf{w}$

Chapter 12: Vectors and the Geometry of Space
Section 2: Vectors
Kaushal Nair
0:00
Calculus

Medians of a triangle Suppose that $A, B,$ and $C$ are the corner points of the thin triangular plate of constant density shown here.
a. Find the vector from $C$ to the midpoint $M$ of side $A B$.
b. Find the vector from $C$ to the point that lies two-thirds of the way from $C$ to $M$ on the median $C M$.
c. Find the coordinates of the point in which the medians of $\Delta A B C$ intersect. According to Exercise $17,$ Section $6.6,$ this point is the plate's center of mass.

Chapter 12: Vectors and the Geometry of Space
Section 2: Vectors
Kaushal Nair
0:00
Calculus

Which do you think will be larger, the average value of
$f(x, y)=x y$ over the square $0 \leq x \leq 1,0 \leq y \leq 1,$ or the aver-
age value of $f$ over the quarter circle $x^{2}+y^{2} \leq 1$ in the first
quadrant? Calculate them to find out.

Chapter 15: Multiple Integrals
Section 3: Area by Double Integration
Kaushal Nair
0:00
Precalculus

Let $f(x)=x^{2}$ and $g(x)=2 x-1$
(a) Compute $\frac{f[g(x)]-f[g(a)]}{g(x)-g(a)}$
(b) Compute $\frac{|| g(x) |-\pi g(a)]}{x-a}$

Chapter 3: Functions
Section 5: Methods of Combining Functions. Iteration
Kaushal Nair
1

Kaushal's Quick Ask Videos

04:59
Intro Stats / AP Statistics

A survey found that women's heights are normally
distributed with mean
62.7 in. and standard deviation 2.1 in. The survey also
found that men's heights are normally distributed with mean
67.5 in. and standard deviation
3.1 in. Most of the live characters employed at an amusement
park have height requirements of a minimum of 57 in. and a maximum
of 63 in. Complete parts (a) and (b) below.
a. Find the percentage of men meeting the
height requirement. What does the result suggest about the genders
of the people who are employed as characters at the
amusement park?
The percentage of men who meet the height requirement is
nothing
%.
(Round to two decimal places as needed.)
Since most men do not meet the height requirement,
it is likely that most of the characters are
women.
b. If the height requirements are changed to
exclude only the tallest 50% of men and the shortest 5%
of men, what are the new height requirements?
The new height requirements are a minimum of in. and a maximum
of in.

Kaushal Nair
04:36
Intro Stats / AP Statistics

A. In one or two sentences describe the study by stating its purpose. Identifying the main dependent and independent variables. Are these variables qualitative or quantitative? Would you classify this study as experimental or observational? Be sure to support your choice of experimental or observational with two to three sentences. Do the results presented in the news article seem plausible? Why? Is there any information in the news article that makes you skeptical about the results? If you had to make a decision about playing music in the workplace, would the results of this study influence your decision on the type of music to play at work? Provide support for or against the results influencing your decision.

B. Define a discrete random variable and define a continuous random variable. Be sure to address random in each definition.

C. Solve the problem and answer the questions.
Problem: Suppose that a couple will have 3 children. Assume that the probability of having a girl is .487 and the probability of having a boy is .513. Also assume that x is a random variable for the number of girls and find the probability where x is 0, 1, 2, or 3. In order words, answer the following probability questions.
What is the probability that none of the three children will be girls?
What is the probability that exactly one of the three will be girls?
What is the probability that exactly two of the three will be girls?
d. What is the probability that all three of the children will be girls?

Kaushal Nair
06:29
Intro Stats / AP Statistics

From a sack of fruit containing 2 bananas, 3 apples, and 2 oranges, a random sample of 4 pieces of fruit is selected. Suppose X is the number of bananas and Y is the number of apples in the sample.
(a) Find the joint probability distribution of X and Y.
(b) Find P[(X,Y)∈A], where A is the region that is given by {(x,y) | x+y≤3}.

Kaushal Nair
07:11
Intro Stats / AP Statistics

7 cards are drawn simultaneously from a standard deck
of 52 cards.
a) What is the size of the sample space?
133784560
b) What is the probability that at
least 3 of cards drawn are red?

Kaushal Nair
02:33
Intro Stats / AP Statistics

In how many ways can 3 boys and 4 girls sit in a row if the boys
and girls must alternate? There __ are nothing ways for them to
sit in a row with boys and girls alternating.

Kaushal Nair
04:45
Intro Stats / AP Statistics

The moment generating function is the expected value of a
continuous random variable X given as Mx (t) = k / (k-t). If E (X2)
= 2/9 then k =? (k> 0) and the variance of X V (X) =?

Kaushal Nair
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