Q1: If a random variable X can have values of -3, -1, 2, and 5 with the respecti

Question

Q1: If a random variable X can have values of -3, -1, 2, and 5 with the respective probabilities: (2k) -3/10, (K)+1/10, (K)-1/10, and (K)-2/10 a) Find distribution table of X, b) The mean(u) and standard deviation (o) of X Q2: A fair coin is tossed until a head or five tails occurs. What is the expected number (E) of tosses of the coin to get those results? Q3: If the lifetime of a transistor in a certain circuit has the following probability density function f(t)-0.1 for t>0 0 otherwise Find the mean and standard deviation of the transistor lifetime.

Explanation / Answer

There are three different type of question, as per chegg guidelines only first question should be solved unless it related to first. here all the three question are indendent.

(1a)

for X to be probability distribution sum of probabilities P(X) should be 1

i..e (2k-3/10) + (k+1/10) + (k-1/10) +( k-2/10)=1

or,5k-5/10=1

or,5k=1.5

or,k=0.3

now the probability distribution and calculation has been given as

mean=E(X)=sum(X*P(X))=-0.4

E(X2)=sum(X2*P(X))=6.4

Var(X)=E(X2)-(E(X))2=6.4-(-0.4)*(-0.4)=6.24

X -3 -1 2 5 P(X) 2k-3/10 k+1/10 k-1/10 k-2/10

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