Complete Question
The complete question is shown on the first and second uploaded image
Answer:
The marginal density function of Y is

The distribution is exponential distribution
and the expected value is
![E[Y] = 10](https://img.qammunity.org/2021/formulas/mathematics/college/5gjcw6i0r7kae09fz41vhy96o0x552eojv.png)
Explanation:
From the question we are told that the function is

Now the marginal density function of Y i.e f(y) is mathematically evaluated by obtaining the probability density function of y as follows



The distribution of the function above is exponential distribution with a rate parameter equals to

The mean DOT estimate E{Y} is mathematically evaluated as
![E[Y] = (1)/(\lambda)](https://img.qammunity.org/2021/formulas/mathematics/college/n3z7fkkhbv84s5fyeva1v5ldou3dajhk13.png)
substituting value
![E[Y] = (1)/((1)/(10) )](https://img.qammunity.org/2021/formulas/mathematics/college/hmpr0rajstugrixwr9jsbiepk3mi0schlc.png)
![E[Y] =10](https://img.qammunity.org/2021/formulas/mathematics/college/ibjht7xkoyq0w0ur1s8cnbwfo1wpdc2hdc.png)