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Evaluate:
Lim↓ n→∞ [ n/1+n² + n/4+ n² +n/9+ n² +...... +n/2n²]
Show that (1/n²+ n+1)↓n∈N
is a Cauchy sequence.
the set of all functions of {1 2 3...,10} to itself forms a group w.r.t the composition of function.true or false
Let
(a↓n)↓n∈ N be any sequence. Show that Lim a↓n =L where n approaches ∞ iff for every ε >0 there exists
some N ∈ N such that n ≥ N implies a↓n ∈ N↓ε (L)
Four coins are tossed. Let T be the random variable representing the number of tails that occur. Construct a probability distribution table and find the probability of picking 2 tails.
A box contains 6 balls labeled form 0 to 5. Three balls are drawn without replacement. Construct the sampling distribution of the following sample statistics of the labels of the balls drawn.
A.sample mean
B.sample range
C.sample max (the highest number in a set)
D.sample min (the lowest numbef in a set)
The product of two divergent sequences is divergent. True or false? Justify.
Give an example of a divergent sequence which has two convergent subsequences.
Justify your claim.
3d²y/dx²+dy/dx-14y=0y(0)=1y(0)=-1
Using the sample space for rolling two dice, construct a probability distribution for the random variable X representing the sum of the numbers that appear.
#339914 on Dec 2023