The annual premium for a $20,000 insurance policy against the theft of a painting is $200. If the (empirical) probability that the painting will be stolen during the year is 0.02, what is your expected return from the insurance company if you take out this insurance? Let X be the random variable for the amount of money received from the insurance company in the given year. E(X) =O dollars

In an uncertain economy, Americans tend to keep spending down. Let x be the amount of money U.S. individuals spend on groceries monthly. Suppose the probability distribution of x is a uniform distribution from $300 to $400 which is represented by the picture below. f(x) 0.010 0.008 0.006 0.004 0.002 300 320 340 360 380 400 X i (a) What is the probability that a randomly selected individual spends between $315 and $370 on groceries each month? (b) Determine whether the following statement is true or false. The variable, the amount an individual plans to spend on groceries per month, is a numerical (quantitative) variable. True O False

An unfair die looks like an ordinary six-sided die but the outcomes are not equally likely. The probability distribution of the face value, XX, is as follows: xixi  1 2 3 4 5 6 Total P(X=xi)P(X=xi)  0.15 0.16 0.33 0.2 0.11 0.05 1 The expected value is computed, E[X]=3.11E[X]=3.11. To find the variance and standard deviation the following table was set up:  xixi   P(X=xi)P(X=xi)   (xi−E[X])2(xi-E[X])2   (xi−E[X])2P(X=xi)(xi-E[X])2P(X=xi)  1 0.15  (1−3.11)2=(−2.11)2=4.4521(1-3.11)2=(-2.11)2=4.4521   4.4521⋅0.15=0.66784.4521⋅0.15=0.6678  2    (2−3.11)2=(−1.11)2=1.2321(2-3.11)2=(-1.11)2=1.2321   1.2321⋅0.16=0.19711.2321⋅0.16=0.1971  3 0.33 (3−3.11)2=(−0.11)2=(3-3.11)2=(-0.11)2=   0.0121⋅0.33=0.0040.0121⋅0.33=0.004  4 0.2  (4−3.11)2=(0.89)2=0.7921(4-3.11)2=(0.89)2=0.7921   0.7921⋅0.2=0.7921⋅0.2=  5    (5−3.11)2=(1.89)2=3.5721(5-3.11)2=(1.89)2=3.5721   3.5721⋅0.11=0.39293.5721⋅0.11=0.3929  6 0.05    8.3521⋅0.05=0.41768.3521⋅0.05=0.4176  E[X]=3.11E[X]=3.11     Total:…

Find the value of X (Left Tailed Probability of 0.5) for v1 = 10 and v2 = 20 degrees of freedom.

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Find the probability ​P(Ec​) if ​P(E)=0.17.

Find the probability of the indicated event if P(E)=0.40 and P(F)=0.55. Find​ P(E or​ F) if​ P(E and ​F)=0.20. ​P(E or F)= _____

Determine whether the following are valid probability models or not. Type "VALID" if it is valid, or type "INVALID" if it is not.