2.5.4A fair coin is tossed four times, and the random variable X is the number of heads in the first three tosses and the random variable Yis the number of heads in the last three tosses. (a) What is the joint probability mass function of X and Y? (b) What are the marginal probability mass functions of X and Y? (c) Are the random variables X and Yindependent? (d) What are the expectations and variances of the random variables X and Y? (e) What is the covariance of X and Y? (f) If there is one head in the last three tosses, what is the conditional probability mass function of X? What are the conditional expectation and variance of X?

Q: please provide the correct answer

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Q: help me with b and c too please

A: The given equatons are b) c)

Q: Please find question attached, Thank you!

A: a) Mean  = n×Π            = 60×(0.65)            = 39 Standard deviation = √(n×Π×(1- Π))…

Q: Can you make your answer clearer

A: 3940, 4060, 3220, 3080, 2920, 3870, 4060, 4030, 3790Arrange in ascending order2920, 3080, 3220,…

Q: only one answer is correct

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Q: 1. Let (x) = x2 + 2. Then (*+h)-f(x) A) 2x + h 2xh+ h2+4 C) B) 1 D) None of the above

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: can you please answer number 7 and show you did the work.

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Q: Please help with #2

A: Given expression is 7xy-4By law of exponent,

Q: where is number 6?

A: Given data :  Desk arranged in 4 rows and 4 columns Probability  of success (p) = 4/16= 1/4 = 0.25…

Q: Please answer all.

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Q: can you write it on a paper or make it clear

A: Apologies for the inconvenience. If you do not see the math expressions properly, then please…

Q: I have a question regarding the question B. Can you please help me? Thanks

A: To use normal approximation, the following conditions should be satisfied. np>5 and n(1-p)>5

Q: Please help lol

A: b) c)

Q: Please answer

A: As per company guidelines we are allowed to solve maximum three sub-parts so i am solving first…