You have been asking several questions over a short period of time. Are you trying to get tutors to do your homework? We can do it, but how do you learn?
In any case, if you walk 2 miles a day, how many miles do you walk in 10 days? 10x2=20, right?
So, what is so difficult...

Your first task is to recognize what probability distribution (either discrete or continuous) is the right one for your particular case.
Here the "experiment" looks at a certain time interval (Saturday morning, 10am -11am) and we are told that ON AVERAGE every such...

Let y = x1/3. Then, I assume you can see that you can write the expression you were given as
y2 - 7y + 12 = 0 (*)
This is a trinomial that you should easily be successful in factoring . If you don't, then there is no point in writing down the full solution...

.. Have you tried taking log() on both sides and using properties of logs?

Well, you are provided with the probability of a strike in the specific region for a specific type of fish, i.e. p = 0.48.
Then, you are told that there is a total of 22 strikes. This info alone should alert you to what is the relevant distribution
you need to use. (22 trials, probability...

Well, it is a somewhat bizarre way to assign a stat problem. I will not solve it for you for in that case you get nothing out of it. But, if you are testing:
H0: p ≤ 0.5 vs. H1: p > 0. 5
Then you reject H0 if a certain statistic is greater than...

Not sure if you mean that you are required to use Taylor's expansions or just compute the limit.
The limit can be computed using L'Hopital's Rule twice and it turns out to be 1/(2π).

Well you start with a function
f(x) = cotg(x) + 4x
compute the first derivative which is the slope of the tangent line at each point x
f'(x) = -1/sin^2(x) + 4
if there exists a point in (o, pi) for which there exists...

It is a binomial random variable, so use the formulas for the binomial.
P(X=k) = n!/(k!(n-k)!) p^k(1-p)^(n-k) n=9, p=0.1 and k=0, 1, .., 9
P(X<4) = P(X=0)+P(X=1)+P(X=2)+ P(X=3).
So use the first formula for k=0, 1, 2, and 3 to find...

You are provided with the right hint.
Let X = number of fatal crashes. You can derive the probability associated with X by using the Number of days
Total number of days = 144+172+128+37+7+1 = 489 (check the calculations!)
Prob. [X=0] = 144/489 = 0...

Let A = "exam covers chapter 1"
B = "exam covers chapter 2"
You know that P(A) = 0.45; P(B) = 0.63, and P(A or B) = 0.76.
You are asked P(A and B) and there is a formula for it,right?
Recall that P(A or B) = P(A) +...

Part (e) cannot be written as
e
∑ n . (*)
n = a
It should be written as
Σn∈{a,e} n (**).
An expression like (*) is ambiguous. In fact, someone who knows the English alphabet...

How about starting from the properties of logs:
a*ln(b) = ln(ab)
ln(a)-ln(b) = ln(a/b)
Also, recall that ln(x) is defined only if x > 0.
So ln(x^2+1) - 3ln(x) = ln(x^2+1) - ln(x^3) = ln(x^2+1/x^3) = ln(2)
...

This problem belongs to the binomial distribution category.
You are interested in the probability that you win at least 7 times out of 12 trials knowing that the probability of success on each attempt is 0.80.
X ~ Bin(n=12, p = 0.80)
and we are looking...

log1/4[(1/4)-2x] = log1/4(64)
-2x = log1/4 64
-2x = log10(64)/log10(1/4) = loge(64)/loge(1/4) = -3
Thus x = 3/2 = 1.5
In fact we can check that (1/4)-2(3/2) = (1/4)-3 = 43 = 64
Remember that to find logaB for any base a, we can always use the logs...

I misunderstood the problem. Sorry.

Well... 10,000 cannot be right. In fact,
log(log(10,000) = log(4) .
Think of it like this:
10log(log(x)) = 104
which is the same as:
log(x) = 104
And therefore x = 10^104 which is a huge number: 1010...

It would have been better if you had shown us what you have done so far. Instead, it seems to me that you are just trying to get your assignment/homework done by the tutors.
How does one solve a system of equations by substitution? We can solve the first equation with
respect...

3
∫ ---------- dx ?
√(4-x2)
but what are the limits of integration? Forget the 3 for a moment, just take the constant out,
and write the denominator as
√4(1-x2/4) = 2√(1-x2/4)
let...

With this kind of problems, one never goes wrong by counting the number of possible outcomes and the number of favorable outcomes.
FAVORABLE OUTCOMES: (2,6), (3,5), (4,4), (5,3), (6,2) ... these sum up to 8.
...